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

0,3

Comments

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

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).

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A183266 A231129 A052722 * A231136 A222003 A139389

Adjacent sequences: A282609 A282610 A282611 * A282613 A282614 A282615

Keyword

nonn,easy

Author

David Nacin, Feb 19 2017

Status

approved