A282612 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to row permutations.

0, 1, 120, 3654, 45760, 333375, 1703016, 6784540, 22500864, 64836045, 167167000, 393877506, 861456960, 1769830699, 3447273480, 6412923000, 11461636096, 19776716505, 33076889784, 53804808190, 85365336000, 132422893911, 201268229800, 300266132244, 440396812800

Offset: 0

Author

David Nacin, Feb 19 2017

Keywords

• nonn
• easy

Comments

Cycle index of symmetry group is (3*s(2)^3*s(1)^3 + 2*s(3)^3 + s(1)^9)/6.

Examples

			The number of 3 X 3 binary matrices up to row permutations is 120.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A282613, A282614, A217331, A168555. A037270 (2x2 version.)

Programs

Mathematica

Table[(3n^6+2n^3+n^9)/6, {n, 0, 24}]

PARI

concat(0, Vec(x*(1 + 110*x + 2499*x^2 + 14500*x^3 + 26015*x^4 + 14934*x^5 + 2365*x^6 + 56*x^7) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017

Formula

a(n) = n^3*(n^3+2)*(n+1)*(n^2-n+1)/6.

G.f.: x*(1 + 110*x + 2499*x^2 + 14500*x^3 + 26015*x^4 + 14934*x^5 + 2365*x^6 + 56*x^7) / (1 - x)^10. - Colin Barker, Feb 23 2017