A250667 -id:A250667 - cp's OEIS frontend

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.

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

Offset: 0

Alois P. Heinz, Nov 26 2014

			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, ...

Alois P. Heinz, Antidiagonals n = 0..100, flattened
Wikipedia, Polyomino

Columns k=0+1,2-10 give: A000012, A005178(n+1), A236577, A236582, A247117, A250663, A250664, A250665, A250666, A250667.

Cf. A251072.

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);

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 *)

A251079 Number of tilings of a 30 X n rectangle using 3n decominoes of shape I.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 89, 225, 415, 665, 981, 1369, 1835, 2385, 3025, 3761, 30169, 79903, 167957, 314911, 548011, 902339, 1422073, 2161837, 3188141, 4580911, 12815576, 31665861, 70135406, 142741143, 272097694, 492367347, 853768306, 1428360119

Offset: 0

Alois P. Heinz, Nov 29 2014

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..100
Wikipedia, Decomino

Column k=10 of A251072.

Cf. A250667.

cp's OEIS Frontend

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.

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