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 A250662 Number A(n,k) of tilings of a 2k X n rectangle using 2n k-ominoes of shape I; square array A(n,k), n>=0, k>=0, read by antidiagonals. 11
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 6, 36, 1, 1, 1, 1, 1, 1, 13, 95, 1, 1, 1, 1, 1, 1, 7, 22, 281, 1, 1, 1, 1, 1, 1, 1, 15, 64, 781, 1, 1, 1, 1, 1, 1, 1, 8, 25, 155, 2245, 1, 1, 1, 1, 1, 1, 1, 1, 17, 37, 321, 6336, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 LINKS Alois P. Heinz, Antidiagonals n = 0..100, flattened Wikipedia, Polyomino EXAMPLE Square array A(n,k) begins: 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 1, 5, 1, 1, 1, 1, 1, 1, ... 1, 1, 11, 6, 1, 1, 1, 1, 1, ... 1, 1, 36, 13, 7, 1, 1, 1, 1, ... 1, 1, 95, 22, 15, 8, 1, 1, 1, ... 1, 1, 281, 64, 25, 17, 9, 1, 1, ... 1, 1, 781, 155, 37, 28, 19, 10, 1, ... 1, 1, 2245, 321, 100, 41, 31, 21, 11, ... MAPLE b:= proc(n, l) option remember; local d, k; d:= nops(l)/2; if n=0 then 1 elif min(l[])>0 then (m->b(n-m, map(x->x-m, l)))(min(l[])) else for k while l[k]>0 do od; `if`(nd+1 or max(l[k..k+d-1][])>0, 0, b(n, [l[1..k-1][], 1\$d, l[k+d..2*d][]])) fi end: A:= (n, k)-> `if`(k=0, 1, b(n, [0\$2*k])): seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA b[n_, l_List] := b[n, l] = Module[{d = Length[l]/2, k}, Which[n == 0, 1, Min[l] > 0 , Function[{m}, b[n-m, l-m]][Min[l]], True, For[k=1, l[[k]] > 0, k++]; If[n d]]] + If[d == 1 || k > d+1 || Max[l[[k ;; k+d-1]]] > 0, 0, b[n, Join[l[[1 ;; k-1]], Array[1&, d], l[[k+d ;; 2*d]]]]]]]; A[n_, k_] := If[k == 0, 1, b[n, Array[0&, 2k]]]; Table[Table[A[n, d-n], {n, 0, d}], {d, 0, 14}] // Flatten (* Jean-François Alcover, Jan 30 2015, after Alois P. Heinz *) CROSSREFS Columns k=0+1,2-10 give: A000012, A005178(n+1), A236577, A236582, A247117, A250663, A250664, A250665, A250666, A250667. Cf. A251072. Sequence in context: A046623 A046602 A282304 * A340366 A031261 A188796 Adjacent sequences: A250659 A250660 A250661 * A250663 A250664 A250665 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Nov 26 2014 STATUS approved

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Last modified May 30 13:17 EDT 2023. Contains 363050 sequences. (Running on oeis4.)