A091060 Number of n X n matrices over symbol set {1,2,3} equivalent under any permutation of row, columns or the symbol set.

1, 1, 8, 139, 15412, 10805764, 50459685390, 1601741458883376, 355089431048672347272, 563306081052639719480623715, 6532991278768207315727662508956920, 564259839851988012635404101255119945332425, 368759675849515285894392091271956490586673272192738

Offset: 0

Author

Christian G. Bower, Dec 17 2003

Keywords

• nonn

Links

• C. G. Bower, Explanation of A091057-A091062

Crossrefs

Cf. A091057-A091062.

Column k=3 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+...=3} (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(11)-a(12) from Alois P. Heinz, Aug 14 2014