OFFSET
1,2
COMMENTS
Number of k X l matrices with entries mod n, up to row and column permutation is Z(S_k X S_l; n,n,...) where Z(S_k X S_l; x_1,x_2,...) is cycle index of Cartesian product of symmetric groups S_k and S_l of degree k and l, respectively.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Marko R. Riedel, Number of equivalence classes of matrices, Math Stackexchange.
Marko R. Riedel, Computing the cycle index for arbitary k x l matrices using Maple
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
a(n) = (1/3!^2)*(n^9 + 6*n^6 + 9*n^5 + 8*n^3 + 12*n^2).
G.f.: x*(12*x^7+369*x^6+2514*x^5+4375*x^4+2360*x^3+423*x^2+26*x+1) / (x-1)^10. - Colin Barker, Jul 09 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Nov 04 2000
STATUS
approved