The On-Line Encyclopedia of Integer Sequences (OEIS)

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

Revision History for A239273

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A239273

Number of domicule tilings of a 2n X 2n square grid.
(history; published version)

#28 by Bruno Berselli at Mon Sep 16 08:23:24 EDT 2019

STATUS

proposed

approved

#27 by Jean-François Alcover at Mon Sep 16 04:59:46 EDT 2019

STATUS

editing

proposed

#26 by Jean-François Alcover at Mon Sep 16 04:59:27 EDT 2019

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 *)

STATUS

approved

editing

#25 by Alois P. Heinz at Sat Dec 01 15:03:23 EST 2018

STATUS

editing

approved

#24 by Alois P. Heinz at Sat Dec 01 15:03:21 EST 2018

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/King%27s_graph">King's graph</a>

#23 by Alois P. Heinz at Sat Dec 01 14:59:50 EST 2018

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KingGraph.html">King Graph</a>

STATUS

approved

editing

#22 by Alois P. Heinz at Fri Nov 23 07:12:40 EST 2018

STATUS

editing

approved

#21 by Alois P. Heinz at Fri Nov 23 07:12:36 EST 2018

DATA

1, 3, 280, 3037561, 3263262629905, 326207195516663381931, 3011882198082438957330143630563, 2565014347691062208319404612723752103028288, 201442620359313683494245316355883565275531844406384955392, 1458834332808489549111708247664894524221330758005874053074138540424018259

EXTENSIONS

a(9) from Alois P. Heinz, Nov 23 2018

STATUS

approved

editing

#20 by Alois P. Heinz at Fri Nov 23 06:58:35 EST 2018

STATUS

editing

approved

#19 by Alois P. Heinz at Fri Nov 23 06:58:30 EST 2018

CROSSREFS

Cf. A004003, A243510, A243424, A220638.

STATUS

approved

editing