A058002 Number of 4 X 4 matrices with entries mod n, up to row and column permutation.

1, 317, 90492, 7880456, 270656150, 4947097821, 58002778967, 490172624992, 3223155968811, 17382581357725, 79840867013666, 321169288917192, 1155731257886192, 3782368364610941, 11406226119319725, 32031530635953536, 84493500676300117, 210856844364222717

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

Formula

a(n)=(1/4!^2)*(n^16 + 12*n^12 + 36*n^10 + 67*n^8 + 160*n^6 + 204*n^4 + 96*n^2).

G.f.: -x*(x +1)*(x^14 +299*x^13 +84940*x^12 +6299584*x^11 +142482546*x^10 +1214416453*x^9 +4351647617*x^8 +6732281120*x^7 +4351647617*x^6 +1214416453*x^5 +142482546*x^4 +6299584*x^3 +84940*x^2 +299*x +1) / (x -1)^17. - Colin Barker, Jul 09 2013

Crossrefs

Cf. A058001, A058003, A058004, A002724, A052271, A052272.

Row n=4 of A246106.

Sequence in context: A273804 A142130 A278279 * A252246 A252254 A252247

Adjacent sequences: A057999 A058000 A058001 * A058003 A058004 A058005

Keyword

easy,nonn

Author

Vladeta Jovovic, Nov 04 2000

Extensions

More terms from Colin Barker, Jul 09 2013

Status

approved