Problem 54345. Fill a rectangle with 1x1 and 2x2 tiles

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>A 3x2 rectangle can be filled with 1x1 and 2x2 tiles in three ways:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"119\"/><w:attr w:name=\"width\" w:val=\"264\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"Tilings of a 3x2 rectangle\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The colors merely distinguish the sizes of the tiles. A 3x3 rectangle can be filled with 1x1 and 2x2 tiles in five ways:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"239\"/><w:attr w:name=\"width\" w:val=\"395\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"Tilings of a 3x3 rectangle\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Write a function to count the ways that a 3x</w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"n\"/></w:customXmlPr><w:r><w:t>n</w:t></w:r></w:customXml><w:r><w:t> rectangle can be filled. 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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

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margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 201.883px 7.50833px; transform-origin: 201.883px 7.50833px; unicode-bidi: normal; "><span style="">A 3x2 rectangle can be filled with 1x1 and 2x2 tiles in three ways:</span></span></div><div style="block-size: 124.65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 62.325px; text-align: left; transform-origin: 384px 62.325px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 264px;height: 119px" src="data:image/png;base64,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" alt="Tilings of a 3x2 rectangle" data-image-state="image-loaded" width="264" height="119"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 354.742px 7.50833px; transform-origin: 354.742px 7.50833px; unicode-bidi: normal; "><span style="">The colors merely distinguish the sizes of the tiles. A 3x3 rectangle can be filled with 1x1 and 2x2 tiles in five ways:</span></span></div><div style="block-size: 244.65px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 122.325px; text-align: left; transform-origin: 384px 122.325px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline;width: 395px;height: 239px" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAxYAAAHeCAIAAACJ+AoAAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAAB9qSURBVHhe7d1drJ3nVSfw9/hjcqxxHCeEjluQcjwUispXihDpRVHGN4OrmYupRkLxBUJGQVXhFi4QChJEXAQJlZHozE07UzGqas1oBo1GnRhVMw0iF2nFh4METcBgl37glsr5MjrH9bE3+y0vW2F0DuzXzvNorXV+P6HwbF9xOPHe//zf9ay9sVgsBgAA5jg0/W8AANYmQgEAzCZCAQDMJkIBAMwmQgEAzCZCAQDMJkIBAMwmQgEAzCZCAQDMJkIBAMwmQgEAzCZCAQDMJkIBAMwmQgEAzCZCAQDMtrFYLKbjfOd+8/PX3vjG9CKt3TuLf/vub3nskft/6be/MP1RTssf5FM/9b0n/sOvDRcvTn+U2qlTwyc/OZ1r+OIzw/Xkv5rF7vDo7169vvP0f39x+pPkfv7ff///ePHrf3r5K9PrtD72wcemUwHLd7BnnpnO2f3f/zO8/JPDN65NLzNa/q1/4PHhwZ8dPvCB6U+y+/CHh0cfnc735p4i1OmnP7t8M51eZPbEe972o9/94PlPvjy9TuvKU49t/cz54cKF6XVqW1vDlSvTuYaXzw/XPj6d83p88fJX3vixX39+epncMnn8xm//6R9efWV6ndaLv/r+6VTAxz42PPnkdM5u+8rw4plh5+r0MqkH3jec/K/D6dPTy+yefXY4e3Y63xsP8kabRwv9/2FzczpAG29s35pOJRw+vDGdgIPg1KnpcM9EqHJ2KvSCRHb/saPTCSCda2/Zc1URqhwtFI0Va6EI5/Dh6QCxiVDAgXb79t3Pg9LE7dvTAVrwII99eZBHY8Ue5JmFgoPFgzz25UEejRV7kKeFAu6OCAUcaFqocMxC0ZQHeezLgzwaK/YgTwsVjlkomvIgj315kEdj9kIBLIlQ5WihYA4tFBwsHuSxLy0UjbmRR1tmoWjKgzz2pYWiMTfyaMssFEmIUOVooWAOLRRwd0SocrRQNOZGHpCYWSj2pYWiMTfyaMssFE2ZhWJfWiiYQwsVjlkokhChytFC0ZgbeQBLIlQ5WigacyMPSMwsFPvSQsEcWqhwzELRlFko9qWFojE38mjLLBRJiFDlaKFozI08gCURqhwtFMyhhYKDxSwU+9JC0ZgbebRlFoqmzEKxLy0UjbmRR1tmoUhChCpHCwVzaKGAuyNClaOFgjm0UHCwmIViX1ooGjMLRVtmoWjKLBT70kLRmFko2jILRRIiVDlaKJhDCwXcHRGqHC0UjdlODiRmFop9aaFozHZy2jILRVNmodiXFgrm0EKFYxaKJESocrRQNLW97UYewJIIVY4WiqaOHXMjD0jMLBT70kLBHFqocMxC0ZRZKPalhYI5tFDhmIUiCRGqHC0UjZmFAlgSocrRQtGYWSggMbNQ7EsLBXNoocIxC0VTZqHYlxaKxmwnpy2zUCQhQpWjhaKp7W3byQGWRKhytFA0dezYdKhCCwUHi1ko9qWFojE38mjLLBRNmYViX1ooGnMjj7bMQpGECFWOFgrm0EIBd0eEKkcLBXNooeBgMQvFvrRQNLW9bRaKtsxC0ZRZKPalhaKpY8fMQtGWWSiSEKHK0ULBHFoo4O6IUOVooWjMdnIgMbNQ7EsLRWO2k9OWWSiaMgvFvrRQMIcWKhyzUCQhQpWjhaIpN/IAvkmEKkcLRVNu5AGpmYViX1oomEMLFY5ZKJoyC8W+tFAwhxYqHLNQJCFClaOFojGzUABLIlQ5Wiia2t42CwUkZhaKfWmhaOrYselQhRYqHLNQNGUWin1poWjMdnLaMgtFEiJUOVooGrOdHGBJhCpHCwVzaKHgYDELxb60UDRlOzmtmYWiqbduFmpjsfBfYMBM29vTXHmiA8BbSoQCAJjNgzwAgNlEKACA2e7pQd7ppz979XqF+19PvOdtT7z7xL/7xOXpdVpXnnps66vnh69dmF6ntrk1PHZlOtdw7txwIf+vZrF47vKrZz7y4vQyuWc/+H2/8um/fP4vXptep7X48OPTKb+Pf+7a+U++PL1IbvmevPzLkv2D8n3/8oHf/amTw2dPT6+z+4H/N5w8M53vjRZq8sqdKndADrmRF1WVy5LHN+5Mp/weLnW5EOhKhBptHi30/4c79kJFVWVl141Fnb8vXy+1JRToSoQa7dyq81/VdVqonavToQwtVDxaKOCuiVCjzaOHHjxU5VuZyrRQm1vTgWAqtVCVfhZoaLE7HXgTbx+jnVt3zELRXJUHeZVaqEo/SxlffcPjVXIQoUZ1ZqF275iFiqvKgzyzUDT13Q/U+Rds947l1ZWJUKM6s1BHDmmhaM0sFE3VeSZAdSLUqM4s1K6nEoG5kRePWSiaOnHUl1hX5u1jVGcW6sihOg/y3MiLyiwUTVWahXr9VpUHeTcfng68iQg1KjULVeZBXr0beVqoeMxCBVRpFqqOzVenA2/i39RRqb1QhKWFiscsVECVZqGOHNo48cb16QXliFCjUnuhoDGzULC+1+9/aDqlZi/UXrx9jMxC0YO9UPGYhQrIXiiyEKFGZqHoocqDvN0jR6ZTfmahAjILRRb+TR2ZhYqo3o28Ko7s1qn0zUIFZC8UWYhQI7NQEbmRF5VZKFiT7eS1efsY1ZmFWjILFZYbefGYhQqo0izUA5tHrl73nlyWCDWqMwu1ZBYqLC1UPGahAqo0C7W4fXvrIe/JZYlQI7NQ9KCFiscsVECVZqHqbCdnLyLUyCwUrM8sFKzJd+TV5u1jVGoWqox6N/LshYrHLFRAlWahNg4fLjIL5Tvy9iJCjUrNQpUZJ693I89eqHjMQgVkFioi35G3FxFqVGcW6sgh4+S0Zi8UTZmFisgXvOxFhBrVmYXa9VQiMDfy4jELRVNmoWrz9jEyC0UPbuTFYxYqILNQZCFCjUrNQhGWFioes1ABmYUiC9FhZC9URPVu5Gmh4jELFZBZKLIQoUal9kK5kUdjZqFgTWahavP2MSo1C+VGXlj2QsVjFiogs1BkIUKNzELRg71Q8ZiFCsgsFFmIDiOzULA+e6FoyixURLaT70WEGpWahSIsN/LiMQtFU3VmoWwn34u3j5G9UBG5kReVWSiaMgsVke3kexGhRqVmodzIC0sLFY9ZqIDMQpGFCDUqNQvlRl5YWqh4zEIFZBaKLESokVkoWJ9ZKFiTvVC1efsYmYWiB3uh4jELFZBZKLIQoUb2QtGDvVDxmIUKyCwUWYgOI3uhIqp3I68Ke6FoyiwUWYhQo1KzUG7kheVGXjxmoWjKLFRt3j5GpWah3MgLy428eMxCBWQWKiLbyfciQo3MQtGDFioes1ABmYWKyHbyvYgOI7NQ9KCFiscsVEBmoSKynXwvItTIXihYn1koWJNZqNq8fYzshYqo3o08e6HiMQsVkFkoshChRqVmodzIC8teqHjMQgVkFoosRKhRqVkoN/JozF4omjILRRYi1MgsFD24kRePWSiaMgtVm7ePkVkoenAjLx6zUAGZhSILEWpkLxQ9aKHiMQsVkFkoshAdRvZCRVTvRp4WKh6zUAGZhYrIdvK9iFCjUrNQbuTRmFkoWFOdWSjbyffi7WNUahbKjbyw7IWKxyxUQGahIrKdfC8i1MgsFD3YCxWPWaiAzEKRhegwMgsF67MXiqbMQpGFCDWyF4oe3MiLxywUTdkLVZu3j5G9UBG5kReVWSiaMgtFFiLUqNQslBt5YWmh4jELFZBZKLIQoUalZqHcyAtLCxWPWaiAzEKRhQg1MgsF6zMLBWsyC1Wbt4+RWSh6sBcqHrNQAZmFish28r2IUCN7oejBXqh4zEIFZBYqItvJ9yI6jOyFiqjejbwq7IWiKbNQEdlOvhcRalRqFsqNvLDcyIvHLBRNmYWqbWOxcF8AAGCee4tQp08PV0s8bXniieHDPzq8fH56mdcP/9nwk08NFy5ML1Pb2hquXJnONXz+3PC1/L+axxfDpUvDe94zvczu2WeHU78yvPb89DKv5e+liv/1e1/+xf/2R9OL5D79C2d+4j++8JVXtqfXOb3jwWPPntsaP/FrWP6tP3t2Ot8bJfY3jXO+VR7kVZlZLsjKrpg26kzHE02NWah3PHRsOvEPiVArlhrAem7cmA4FHD8+HaCBGrNQt2/XGvg5dWo63DMRasVqTRorM+lfKXZUioPAOq5dmw73TIRa0ULRWJkHeVooWM8rf2PzWGUi1IoWCtZTLHZYeEMzD/5zm8cqE6FWtFA0VuZBXqUWavmzGCeHA8UsVANaKBor8yCvUgvlQR4teZAXkVmoBrRQNKaFCsg4OS15kFebCLWihaIxLVRAWihaqvMdeexFhFrRQsF6tFCwHt+RF5FZqAa0UDRmL1RAWihaMgsVkVmoBrRQNGYvVEBaKFoyC1WbCLWihYL1aKEARKg30ULRmBt5AWmhaMmDvIjMQjWghaIxN/IC0kLRkgd5EZmFakALRWNaqIC0ULRkqUFtItSKForGtFABaaGiubM9HUqw1KA2EWpFCwXr0ULRzqFj06EEs1ARmYVqQAtFY/ZCBaSFoiWzUBGZhWpAC0Vj9kIFpIWipddvLb7ySqlHk7yZCLWihYL1aKFop9ws1DseLPVokjcToVa0UDTmRl5AWqhoas1CEZFZqAa0UDTmRl5AWiga8yAvHLNQDWihaEwLFZAWisY8yCtMhFrRQtGYFiogLVQ0tWahqE2EWtFCwXq0ULRTbhbKg7xwzEI1oIWiMXuhAtJC0ZgHeeGYhWpAC0Vj9kIFpIUC7pYItaKFgvVooWin3CyUB3mFiVArWigacyMvIC1UNOVmoTzIC8csVANaKBpzIy8gLRQcNGahGtBC0ZgWKiAtFC35jrzaRKgVLRSNaaEC0kJFU2sW6p1HbnqQV5gItaKFgvVooWin1izU5d37phNxmIVqQAtFY/ZCBaSFoqUTRzemE3GYhWpAC0Vj9kIFpIWipddvLaYTFYlQK1ooWI8WinZqzUJpoWoToVa0UDTmRl5AWqhoas1CuZEXkVmoBrRQNOZGXkBaKFo6cXTDjbxwzEI1oIWiMS1UQFqoaHzBC3mIUCtaKBrTQgWkhYrGF7yQhwi1ooWC9WihYG1aqHDMQjWghaIxe6EC0kJFU+tB3tsWO1qocMxCNaCFojF7oQLSQkVjOzl5iFArWihYjxYK1mMvVG0i1IoWisbcyAtICxVNrQd59kJFZBaqAS0UjbmRF5AWKppaD/LeeeSmWahwzEI1oIWiMS1UQFooWjILVZsItaKFojEtVEBaqGh8Rx55iFArWihYjxaKdsp9R950Ig6zUA1ooWjMXqiAtFC0pIWKyCxUA1ooGrMXKiAtVDRu5JGHCLWihYL1aKFop9aDvBNHN9zIK0yEWtFC0ZgbeQFpoWhMCxWOWagGtFA05kZeQFqoaGo9yFvSQoVjFqoBLRSNaaEC0kJFU+tB3pIWqjARakULRWNaqIC0UDSmhSpMhFrRQsF6tFC0U+5BHuGYhWpAC0Vj9kIFpIWKptaDvLctdjzIC8csVANaKBqzFyogLRQtXd69z4O8wkSoFS0UrEcLRTu+I488RKgVLRSNuZEXkBYqmnI38gjHLFQDWigacyMvIC0UjZmFCscsVANaKBrTQgWkhYrGak3yEKFWtFA0poUKSAsVjQd55LGxWCym4124dGkqxE6dyn3Y3By+65Hh9RfGl3kdeXA4/ujw0kvD1avr/uCRD8t/Pvro+LKM7cvj//yzU8M3rg2H7pv+MJ2TZ4bt7eF3fmcMHzdu/NO/x+CHra3hyNVh95XxZWrL30sVl7++/eprUxf15Ve2v+3vW5yM5x86fez3rqTv1R75F/d/6/Gjw8WL44s1/2ZFPpw9O57fCvcWoYD1LZPHsW++sa4OwH7ubO/dSGX/cwoRoQAAZjMLBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAwmwgFADCbCAUAMJsIBQAw28ZisZiOVHLpR4bXnp/OeT2+GC5eHN7//ulldleuDF84PZ1TW/5eKjl3brhwYTqntrU1/Mmnh8995/Qyr3d9dPjUMDz55PQyu+Vf/OWvhoq0UNDL5uawmf+dtMCPAPBWEKGgl52dYefqdAYgORGK2I4fnw4F1Gih6qXA5e8FYD4Rithu3JgOBFHvQd7OznQo4ObD0wFoT4QitkotVKWP6koqtVCbr06H7A4fng4QmAhFbFooWhNtA7p9ezpAYCIUsVVqoWowCxXZYnc6ZKeFIgMRitiKtVAF8odZqMg2jkyH7LRQZCBCFVXmndSNPFrTQgWkhSIDEaqoMu+kZqForVILdd+3TYfstFBkIEIRmxt50ZiFiuzml6dDdlooMhChiE0LFY1ZKDrQQpGBCEVsbuTRWqUWqgwtFBmIUMSmhaI1N/IC0kKRgQhVlBt5NGIWKjI38qAjEaooN/JoxCxUZG7kQUciFLFpoWjNjbyAtFBkIEIRmxaK1tzIC0gLRQYiFLFpoaIxC0UHWigyEKGITQsVjVkoOtBCkYEIVZQbebCmUrNQD0+H7LRQZCBCFeVGHqypUgu1+ep0yE4LRQYiFLFpoaIxCxWZvVDQkQhFbFqoaMxCRWY7OXQkQhGbForWtFABaaHIQIQiNi0UrWmhAtJCkYEIVZQbeTRiFioyLRR0JEIV5UYejZiFisx35EFHIhSxaaFordReKN+RB/2IUMSmhaI128kD0kKRgQhFbFqoaMxC0YEWigxEKGLTQkVjFooOtFBkIEIV5UYerKnULJTvyIN+RKii3MiDNVVqoXxHHnQkQhGbFioas1CR2QsFHYlQxKaFisYsVGS2k0NHIhSxaaFoTQsVkBaKDEQoYtNC0ZoWKiAtFBmIUEW5kUcjZqEi00JBRyJUUW7k0YhZqMh8Rx50JEIRmxaK1krthfIdedCPCEVsWihas508IC0UGYhQxKaFisYsFB1oochAhCI2LVQ0ZqHoQAtFBiJUUW7kwZpKzUL5jjzoR4Qqyo08WFOlFsp35EFHIhSxaaGiMQsVmb1Q0JEIRWxaqGjMQkVmOzl0JEIRmxaK1rRQAWmhyECEIjYtFK1poQLSQpGBCFWUG3k0YhYqMi0UdCRCFeVGHo2YhYrMd+RBRyIUsWmhaK3UXijfkQf9iFDEpoWiNdvJA9JCkYEIRWxaqGjMQtGBFooMRChi00JFYxaKDrRQZCBCFeVGHqyp1CyU78iDfkSootzIgzVVaqF8Rx50JEIRmxYqGrNQkdkLBR2JUMSmhYrGLFRktpNDRyIUsWmhaE0LFZAWigxEKGLTQtGaFiogLRQZiFBFuZFHI2ahItNCQUcbi8ViOlLJy+crfNT9wGeGl14aPvSh6WV2v/Vbw199aLj5pdwBd3NreNd/mc41PPPMcPHidE7t1KnhE/95+KN/PZ5T/zv2yC8OL9wcfy81LP/inzw5nalFhAIAmM2DPACA2UQoAIDZPMgr6tKl4dq18XD8+HipLdc/V/9nnz371zdu/fG1vxn/JL8f/Pbjf/Cl8afb2b3zd3+S0cNHhx/6joemFzXcuDTsvjKdUzvy4LC7Nbzwwnj+//4q5To8/vhw8+Yw/OF4LuDEe4dDx6YztYhQRZ05Mzz33HTOa7F47vKrZz7y4vQyuStPPbb8Wa5ez32FfuuhzeUPMr2o4fPnhq9dmM7Zveuvhre/fTrn9dGPDv9mGF5+cnqZ3Q//2XDsndOZWjzIAyih3uJ4iE2EAg62Q4X2QlVaEwrhiVDAwXZH7ADuhggFHGyVWqg6bCcnAREKONi0UBH5jjwSEKGAGbLfKNyDFioiLRQJiFDADFsPlQscWqiItFAkIEJBL5k3aq6ceOP6dCpDCxWRFooERCjo5UiFv26v319rNfmSFioiLRQJiFDQS4kWqiAtVERaKBIQoaCXEi1UQVqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy8lWih7oehCC0UCIhT0UqKFsheKLrRQJCBCQS/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS9u5MWkhYpIC0UCIhT04kZeTFqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS9u5MWkhYpIC0UCIhT04kZeTFqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS9u5MWkhYpIC0UCIhT04kZeTFqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS9u5MWkhYpIC0UCIhT04kZeTFqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS9u5MWkhYpIC0UCIhT04kZeTFqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJCBCQS9u5MWkhYpIC0UCIhT04kZeTFqoiLRQJOA9HXrRQsWkhYpIC0UCIhT0ooWKSQsVkRaKBLynQy/2QsWkhYpIC0UCIhT0Yi9UTFqoiLRQJLCxWCymI5WcPz9cvTqd8/rMZ65e3/nxT7w0vUzuf57/np/7zd//89u5I8h3HN75+E+/d3pRwxefGa5fnM55LXaH+759ePt/Gj7wgelP8nr66eF7bw1f+OXpZWrL38vW/x5OnpxeUosIVdTO1WHnynTO6+SZ13d2/+BLN45v3LmxOJT9n//qnSefu/zq8sda/eHXbw0PHx1/0PiH1U+xefTQex85Mf5RGS+9NP73xvHjw40buf+59L73Da9+5ps/VWYnz4y/keXv5R/5YRP98+zZ6eeiHBGqqEs/Mrz2/HTO6/HFMnOc+ciL08vkrjz12PJnyT5LtPXQ5vIHmV7UcO7ccOHCdE5ta2v4k08Pn/vO6WVe7/ro8KlhePLJ6WV2V66MvxoqMgsFUMXGkekAtCdCAQfbpht58Rx2I48ERCjgYNtxIy+e227kkYAIBcxQcC+UFiogLRQZiFDADAX3QmmhAtJCkYEIRWg7vlcumBNvXJ9OZWihAtJCkYEIRWibvlcumNfvf2g6laGFCkgLRQY+n4qqcrdZC0VzWqiAtFBkIEIVtdidDslpoWhOCxWQFooMfD4RmhaK5rRQAWmhyECEIjQtFM1poQLSQpGBzydC00JFYy8UPWihyECEIjQtVDT2QtGDFooMfD4V5UYebdgLRQ9aKDIQoYpyI4827IWiBy0UGfh8IjQtFM1poQLSQpGBCEVoWiia00IFpIUiA59PhKaFojktVEBaKDIQoQhNC0VzWqiAtFBk4POpKDfyaMNeKHrQQpGBCFWUG3m0YS8UPWihyMDnE6FpoaKxF4oetFBkIEIRmhYqGnuh6EELRQY+nwhNC0VzWqiAtFBkIEIRmhaK5rRQAWmhyMDnU1Fu5MGatFABaaHIQIQqyo08WJMWKiAtFBn4fCI0LVQ09kLRgxaKDEQoQtNCRWMvFD1oocjA5xOhaaGisReKHrRQZCBCEZoWKhp7oehBC0UGPp+KciMP1qSFCkgLRQYiVFFu5MGatFABaaHIwOcToWmhaE4LFZAWigxEKELTQtGcFiogLRQZ+HwiNC1UNPZC0YMWigxEKELTQkVjLxQ9aKHIwOdTUW7k0Ya9UPSghSIDEaooN/Jow14oetBCkYHPJ0LTQtGcFiogLRQZiFCEpoWiOS1UQFooMvD5RGhaKJrTQgWkhSIDEYrQtFA0p4UKSAtFBj6finIjjzbshaIHLRQZiFBFuZFHG/ZC0YMWigx8PhGaFioae6HoQQtFBiIUoWmhorEXih60UGTg84nQtFA0p4UKSAtFBiIUoWmhaE4LFZAWigx8PhXlRh6sSQsVkBaKDESootzIgzVpoQLSQpGBzydC00JFYy8UPWihyECEIjQtVDT2QtGDFooMfD4RmhYqGnuh6EELRQYiFKFpoaKxF4oetFBk4POpKDfyYE1aqIC0UGQgQhXlRh6sSQsVkBaKDHw+EZoWiua0UAFpochAhCI0LRTNaaEC0kKRgc8nQtNCRWMvFD1oochAhCI0LVQ09kLRgxaKDHw+FeVGHm3YC0UPWigyEKGKciOPNuyFogctFBn4fCI0LRTNaaEC0kKRgQhFaFoomtNCBaSFIoONxWIxHQEAWI//xAcAmE2EAgCYTYQCAJhNhAIAmE2EAgCYTYQCAJhNhAIAmE2EAgCYTYQCAJhNhAIAmE2EAgCYTYQCAJhNhAIAmE2EAgCYTYQCAJhNhAIAmE2EAgCYTYQCAJhNhAIAmGkY/hYrs2REApw+SAAAAABJRU5ErkJggg==" alt="Tilings of a 3x3 rectangle" data-image-state="image-loaded" width="395" height="239"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.658px 7.50833px; transform-origin: 133.658px 7.50833px; unicode-bidi: normal; "><span style="">Write a function to count the ways that a 3x</span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">n</span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 73.9083px 7.50833px; transform-origin: 73.9083px 7.50833px; unicode-bidi: normal; "><span style=""> rectangle can be filled. </span></span></div></div></div>

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Problem 54345. Fill a rectangle with 1x1 and 2x2 tiles

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Problem 54345. Fill a rectangle with 1x1 and 2x2 tiles

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