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

Author

David Nacin, Feb 19 2017

Keywords

• nonn
• easy

Comments

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

Examples

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

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. (For 2x2 version see A039623.)

Programs

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 *)

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

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