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
Examples
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.
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).