A306100 Square array T(n,k) = number of plane partitions of n with parts colored in (at most) k colors; n >= 0, k >= 0; read by antidiagonals.

1, 1, 0, 1, 1, 0, 1, 2, 3, 0, 1, 3, 10, 6, 0, 1, 4, 21, 34, 13, 0, 1, 5, 36, 102, 122, 24, 0, 1, 6, 55, 228, 525, 378, 48, 0, 1, 7, 78, 430, 1540, 2334, 1242, 86, 0, 1, 8, 105, 726, 3605, 8964, 11100, 3690, 160, 0, 1, 9, 136, 1134, 7278, 25980, 56292, 47496, 11266, 282, 0

Offset: 0

Author

M. F. Hasler, Sep 22 2018

Keywords

• nonn
• tabl

Examples

			The array starts:
  [1  1    1     1     1      1 ...] = A000012
  [0  1    2     3     4      5 ...] = A001477
  [0  3   10    21    36     55 ...] = A014105
  [0  6   34   102   228    430 ...] = A067389
  [0 13  122   525  1540   3605 ...]
  [0 24  378  2334  8964  25980 ...]
  [0 48 1242 11100 56292 203280 ...]
		

Links

• Alois P. Heinz, Antidiagonals n = 0..50, flattened
• OEIS wiki, Plane partitions.
• Wikipedia, Plane partition.

Crossrefs

Columns k=0-5 give: A000007, A000219, A306099, A306093, A306094, A306095.

See A306101 for a variant.

Cf. A091298, A208447, A001477, A014105, A067389.

Programs

PARI

A306100(n,k)=sum(j=1,n,A091298(n,j)*k^j)

Formula

T(n,k) = Sum_{j=0..n} A091298(n,j)*k^j, assuming A091298(n,0) = A000007(n).

T(n,k) = Sum_{i=0..k} C(k,i) * A319600(n,i). - Alois P. Heinz, Sep 28 2018

Extensions

Edited by Alois P. Heinz, Sep 26 2018