A282614 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to vertical and horizontal reflections.

0, 1, 168, 5346, 67840, 496875, 2544696, 10151428, 33693696, 97135605, 250525000, 590412966, 1291500288, 2653631071, 5169160920, 9616725000, 17188519936, 29659392873, 49607301096, 80696066410, 128032800000, 198613915731, 301875282808, 450363792396

Offset

0,3

Comments

Cycle index of symmetry group is (2*s(2)^3*s(1)^3 + s(2)^4*s(1) + s(1)^9)/4.

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^5*(n+1)*(n^3-n^2+n+1)/4.

G.f.: x*(1 + 158*x + 3711*x^2 + 21820*x^3 + 39095*x^4 + 22254*x^5 + 3577*x^6 + 104*x^7) / (1 - x)^10. - Colin Barker, Feb 23 2017

Example

The number of 3 X 3 binary matrices up to vertical and horizontal reflections is 168.

Mathematica

Table[(2n+1+n^4)n^5/4, {n, 0, 24}]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 168, 5346, 67840, 496875, 2544696, 10151428, 33693696, 97135605}, 30] (* Harvey P. Dale, Oct 01 2024 *)

Prog

(PARI) concat(0, Vec(x*(1 + 158*x + 3711*x^2 + 21820*x^3 + 39095*x^4 + 22254*x^5 + 3577*x^6 + 104*x^7) / (1 - x)^10 + O(x^30))) \\ Colin Barker, Feb 23 2017

Crossrefs

Cf. A282613, A282614, A217331, A168555. (For 2x2 version see A039623.)

Sequence in context: A331908 A231995 A223243 * A003807 A011785 A227433

Adjacent sequences: A282611 A282612 A282613 * A282615 A282616 A282617

Keyword

nonn,easy

Author

David Nacin, Feb 19 2017

Status

approved