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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`(n<d, 0, b(n, subsop(k=d, l)))+

         `if`(d=1 or k>d+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, 0, b[n, ReplacePart[l, k -> 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-Fran├žois 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 June 18 23:16 EDT 2021. Contains 345125 sequences. (Running on oeis4.)