A056037 Number of 6x6 binary matrices with n ones, with no zero rows or columns, up to row and column permutation.

1, 2, 15, 69, 288, 840, 2144, 4488, 8317, 13160, 18636, 23078, 25856, 25623, 23187, 18713, 13932, 9288, 5816, 3256, 1767, 858, 419, 180, 88, 34, 16, 6, 3, 1, 1

Offset: 6

Author

Vladeta Jovovic, Aug 04 2000

Keywords

• fini
• full
• nonn

Comments

Sum_{k=0..36} a(n)=A054976(6).

Crossrefs

Cf. A052370.

Formula

G.f. : Z(S_6 X S_6; x_1, x_2, ...)-2*Z(S_6 X S_5; x_1, x_2, ...)+Z(S_5 X S_5; x_1, x_2, ...) if we replace x_i by 1+x^i, where Z(S_i X S_j; x_1, x_2, ...) is cycle index of Cartesian product of symmetric groups S_i and S_j of degree i and j, respectively.