A091062 Number of n X n matrices over symbol set {1,2,3,4,5} equivalent under any permutation of row, columns or the symbol set.

1, 1, 9, 649, 2283123, 173636442196, 234378355489344704, 5830719097591168695360621, 2779203181367458204944451774688032, 26174539685600184383643311230836752183522328, 4992259182572292655057303928366260085844535079288641049

Offset: 0

Author

Christian G. Bower, Dec 17 2003

Keywords

• nonn

Links

• C. G. Bower, Explanation of A091057-A091062
• Index to number of inequivalent matrices modulo permutation of row and columns

Crossrefs

Cf. A091057-A091061.

Column k=5 of A242095.

Formula

a(n) = sum_{1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n, 1*u_1+2*u_2+...=5} (fixA[s_1, s_2, ...;t_1, t_2, ...;u_1, u_2, ...]/(1^s_1*s_1!*2^s_2*s_2!* ... *1^t_1*t_1!*2^t_2*t_2!* ... *1^u_1*u_1!*2^u_2*u_2!*...)) where fixA[...] = prod_{i, j>=1} ( (sum_{d|lcm(i, j)} (d*u_d))^(gcd(i, j)*s_i*t_j)).

Extensions

a(10) from Alois P. Heinz, Aug 14 2014