The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A239273 Number of domicule tilings of a 2n X 2n square grid. 4
 1, 3, 280, 3037561, 3263262629905, 326207195516663381931, 3011882198082438957330143630563, 2565014347691062208319404612723752103028288, 201442620359313683494245316355883565275531844406384955392, 1458834332808489549111708247664894524221330758005874053074138540424018259 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A domicule is either a domino or it is formed by the union of two neighboring unit squares connected via their corners. In a tiling the connections of two domicules are allowed to cross each other. Number of perfect matchings in the 2n X 2n kings graph. - Andrew Howroyd, Apr 07 2016 LINKS Table of n, a(n) for n=0..9. Eric Weisstein's World of Mathematics, King Graph Wikipedia, King's graph FORMULA a(n) = A239264(2n,2n). EXAMPLE a(1) = 3: +---+ +---+ +---+ |o o| |o o| |o-o| || || | X | | | |o o| |o o| |o-o| +---+ +---+ +---+. a(2) = 280: +-------+ +-------+ +-------+ +-------+ +-------+ |o o o-o| |o o o-o| |o-o o-o| |o o o o| |o o-o o| | X | | X | | | | X | || | \ / | |o o o o| |o o o o| |o o o o| |o o o o| |o o o o| | / || | / / | || X || | | || || |o o o o| |o o o o| |o o o o| |o-o o o| |o o o o| || \ | || || | | | X | | / / | |o o-o o| |o o-o o| |o-o o-o| |o-o o o| |o o o-o| +-------+ +-------+ +-------+ +-------+ +-------+ ... MATHEMATICA b[n_, l_List] := b[n, l] = Module[{d = Length[l]/2, f = False, k}, Which[n == 0, 1, l[[1 ;; d]] == Array[f &, d], b[n - 1, Join[l[[d + 1 ;; 2*d]], Array[True &, d]]], True, For[k = 1, ! l[[k]], k++]; If[k < d && n > 1 && l[[k + d + 1]], b[n, ReplacePart[l, {k -> f, k + d + 1 -> f}]], 0] + If[k > 1 && n > 1 && l[[k + d - 1]], b[n, ReplacePart[l, {k -> f, k + d - 1 -> f}]], 0] + If[n > 1 && l[[k + d]], b[n, ReplacePart[l, {k -> f, k + d -> f}]], 0] + If[k < d && l[[k + 1]], b[n, ReplacePart[l, {k -> f, k + 1 -> f}]], 0]]]; A[n_, k_] := If[Mod[n*k, 2]>0, 0, If[k>n, A[k, n], b[n, Array[True&, k*2]]]]; a[n_] := A[2n, 2n]; Table[Print[n]; a[n], {n, 0, 7}] (* Jean-François Alcover, Sep 16 2019, after Alois P. Heinz in A239264 *) CROSSREFS Even bisection of main diagonal of A239264. Cf. A004003, A243510, A243424, A220638. Sequence in context: A263884 A096126 A057599 * A054583 A139984 A057631 Adjacent sequences: A239270 A239271 A239272 * A239274 A239275 A239276 KEYWORD nonn AUTHOR Alois P. Heinz, Mar 13 2014 EXTENSIONS a(8) from Alois P. Heinz, Sep 30 2014 a(9) from Alois P. Heinz, Nov 23 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 15 12:56 EDT 2024. Contains 374332 sequences. (Running on oeis4.)