A091061 Number of n X n matrices over symbol set {1,2,3,4} equivalent under any permutation of row, columns or the symbol set.

1, 1, 9, 408, 332034, 3327329224, 382430372929443, 521184164586987473279, 8728898357751671813141271503, 1850296785573740600565249566845514268, 5085095493754879591102840109774321148107411672, 184819445887199812520846920949561110945504502827686252918

Offset

0,3

Links

Table of n, a(n) for n=0..11.

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+...=4} (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.

Column k=4 of A242095.

Sequence in context: A151632 A035024 A179433 * A024123 A218140 A292073

Adjacent sequences: A091058 A091059 A091060 * A091062 A091063 A091064

Keyword

nonn

Author

Christian G. Bower, Dec 17 2003

Extensions

a(11) from Alois P. Heinz, Aug 14 2014

Status

approved