A363685 Irregular triangle read by rows: T(n,k) is the number of descending plane partitions of order n with the sum of the parts equal to k.

1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 2, 3, 2, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 3, 4, 4, 7, 7, 10, 11, 14, 14, 18, 18, 21, 21, 23, 22, 25, 22, 23, 21, 21, 18, 18, 14, 14, 11, 10, 7, 7, 4, 4, 3, 2, 1, 1, 0, 1

Offset

1,18

Links

Table of n, a(n) for n=1..75.

Formula

T(0, 0) = 1, T(1, 0) = 1, T(n, k) = 0 for k < 0 or k > (1/3)*(n+1)*n*(n-1).

Example

Rows 1 through 5 are
  1;
  1, 0, 1;
  1, 0, 1, 1, 1, 1, 1, 0, 1;
  1, 0, 1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 2, 3, 2, 2, 1, 1, 0, 1;
  1, 0, 1, 1, 2, 3, 4, 4, 7, 7, 10, 11, 14, 14, 18, 18, 21, 21, 23, 22, 25, 22, 23, 21, 21, 18, 18, 14, 14, 11, 10, 7, 7, 4, 4, 3, 2, 1, 1, 0, 1.

Crossrefs

Row sums give A005130.

Cf. A198890, A005130, A064999.

Sequence in context: A106737 A359360 A323164 * A339666 A318881 A280338

Adjacent sequences: A363682 A363683 A363684 * A363686 A363687 A363688

Keyword

nonn,tabf

Author

Ludovic Schwob, Jun 15 2023

Status

approved