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 A302484 Number of Truchet tilings of an n X n square up to rotation and reflection. 0
 1, 1, 43, 32896, 536911936, 140737496743936, 590295810401655390208, 39614081257132309534260330496, 42535295865117307944451040976113238016, 730750818665451459101843020821051317142553624576, 200867255532373784442745261543437606940418017880259520626688 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A Truchet tile is a unit square split along the diagonal into two triangles, one black and the other white. It has four orientations, with the white half at the NW, NE, SE, and SW. There are 4^(n^2) ways to tile an n X n square with Truchet tiles if rotations and reflections are counted as different. The number of tilings up to symmetry can be found using Burnside's lemma. LINKS Table of n, a(n) for n=0..10. Eric Weisstein's World of Mathematics, Truchet Tiling Wikipedia, Truchet tiles FORMULA a(n) = (4^(n^2) + 5*4^(n^2/2) + 2*4^(n^2/4)) / 8 if n is even. a(n) = (4^(n^2) + 2*4^(n^2/2)) / 8 if n is odd. MATHEMATICA f[n_]:=If[EvenQ[n], (4^(n^2) + 5 4^(n^2/2) + 2 4^(n^2/4))/8, (4^(n^2) + 2 4^(n^2/2))/8]; Join[{1}, Array[f, 60]] (* Vincenzo Librandi, Apr 09 2018 *) PROG (Python) def a(n): return (4**(n*n)+2**(n*n+1))//8 if n%2 else (4**(n*n)+5*4**(n*n//2)+2*4**(n*n//4))//8 CROSSREFS Sequence in context: A356203 A184144 A262856 * A177488 A262648 A185558 Adjacent sequences: A302481 A302482 A302483 * A302485 A302486 A302487 KEYWORD nonn,easy AUTHOR David Radcliffe, Apr 08 2018 STATUS approved

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Last modified June 2 10:25 EDT 2023. Contains 363097 sequences. (Running on oeis4.)