A091059 Number of n X n matrices over symbol set {1,2} equivalent under any permutation of row, columns or the symbol set.

1, 1, 5, 18, 173, 2812, 126446, 16821330, 7343033248, 10733521835504, 52867612881649880, 882178115128903807148, 50227997322259477864188380, 9837048598740464300126599181536, 6681839615514161335727724211992609234, 15867777966020615016155969700335142344866474

Offset: 0

Author

Christian G. Bower, Dec 17 2003

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20
• C. G. Bower, Explanation of A091057-A091062
• Index to number of inequivalent matrices modulo permutation of rows and columns

Crossrefs

Cf. A091057-A091062.

Main diagonal of A242093.

Column k=2 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=2} (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(15) from Alois P. Heinz, Aug 14 2014