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

0,3

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

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)).

Crossrefs

Cf. A091057-A091062.

Main diagonal of A242093.

Column k=2 of A242095.

Sequence in context: A204252 A281564 A291356 * A352663 A203180 A359616

Adjacent sequences: A091056 A091057 A091058 * A091060 A091061 A091062

Keyword

nonn

Author

Christian G. Bower, Dec 17 2003

Extensions

a(15) from Alois P. Heinz, Aug 14 2014

Status

approved