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 A322495 Number of tilings of an n X n square using V (2m+1)-ominoes (m >= 0) in standard orientation. 1
 1, 1, 2, 8, 68, 1262, 51420, 4577274, 888837716, 376116199534, 346688563051200, 695975307003529228 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The shapes of the tiles are: ._. ._. | | ._. | | | | ._. | |_. | |_._. | |_._._. |_| |___| |_____| |_______| ... . LINKS Table of n, a(n) for n=0..11. Wikipedia, Polyomino EXAMPLE a(3) = 8: ._____. ._____. ._____. ._____. ._____. ._____. ._____. ._____. |_|_|_| | |_|_| |_|_|_| |_| |_| |_|_|_| |_| |_| | |_|_| | | |_| |_|_|_| |___|_| | |_|_| |_|___| |_| |_| | |___| | |_|_| | |___| |_|_|_| |_|_|_| |___|_| |_|_|_| |_|___| |___|_| |_____| |_____|. . MAPLE b:= proc(n, l) option remember; local k, m, r; if n=0 or l=[] then 1 elif min(l)>0 then (t-> b(n-t, map(h->h-t, l)))(min(l)) elif l[-1]=n then b(n, subsop(-1=[][], l)) else for k while l[k]>0 do od; r:= 0; for m from 0 while k+m<=nops(l) and l[k+m]=0 and n>m do r:= r+b(n, [l[1..k-1][], 1\$m, m+1, l[k+m+1..nops(l)][]]) od; r fi end: a:= n-> b(n, [0\$n]): seq(a(n), n=0..9); MATHEMATICA b[n_, l_] := b[n, l] = Module[{k, m, r}, Which[n == 0 || l == {}, 1, Min[l] > 0, Function[t, b[n-t, l-t]][Min[l]], l[[-1]] == n, b[n, ReplacePart[l, -1 -> Nothing]], True, For[k = 1, l[[k]] > 0, k++]; r = 0; For[m = 0, k + m <= Length[l] && l[[k+m]] == 0 && n > m, m++, r = r + b[n, Join[l[[1 ;; k-1]], Array[1&, m], {m+1}, l[[k+m+1 ;; Length[l]]]]]]; r]]; a[n_] := b[n, Array[0&, n]]; a /@ Range[0, 9] (* Jean-François Alcover, Apr 22 2021, after Alois P. Heinz *) CROSSREFS Main diagonal of A322494. Sequence in context: A157752 A055547 A113087 * A332637 A239843 A099729 Adjacent sequences: A322492 A322493 A322494 * A322496 A322497 A322498 KEYWORD nonn,more AUTHOR Alois P. Heinz, Dec 12 2018 STATUS approved

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Last modified April 17 07:59 EDT 2024. Contains 371756 sequences. (Running on oeis4.)