Problem 44735. Aztec Diamond domino tilings
Consider a Cartesian grid, with verteces at integer x and y values, where every four vertices around a vacant space define a unit square. An Aztec Diamond of order d is the shape formed by all unit squares whose centers satisfy the equation:
abs(x) + abs(y) <= d
Given the order of an Aztec Diamond, d (positive integer), return the number, n, of possible tilings using domino tiles, i.e. rectangles sized 1x2 and 2x1, such that:
- The entire shape is covered
- There are no overlapping tiles
- None of the tiles stick out of the shape
Example:
An Aztec Diamond of order 4 is shown at this URL.
Input: d = 4
Output: n = 1024
Solution Stats
Solution Comments
Show commentsProblem Recent Solvers12
Suggested Problems
-
Sort a list of complex numbers based on far they are from the origin.
5648 Solvers
-
1011 Solvers
-
348 Solvers
-
Simple equation: Annual salary
4187 Solvers
-
67 Solvers
More from this Author45
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!