This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282614 #12 Oct 01 2024 13:20:45
%S A282614 0,1,168,5346,67840,496875,2544696,10151428,33693696,97135605,
%T A282614 250525000,590412966,1291500288,2653631071,5169160920,9616725000,
%U A282614 17188519936,29659392873,49607301096,80696066410,128032800000,198613915731,301875282808,450363792396
%N A282614 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to vertical and horizontal reflections.
%C A282614 Cycle index of symmetry group is (2*s(2)^3*s(1)^3 + s(2)^4*s(1) + s(1)^9)/4.
%H A282614 Colin Barker, <a href="/A282614/b282614.txt">Table of n, a(n) for n = 0..1000</a>
%H A282614 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F A282614 a(n) = n^5*(n+1)*(n^3-n^2+n+1)/4.
%F A282614 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
%e A282614 The number of 3 X 3 binary matrices up to vertical and horizontal reflections is 168.
%t A282614 Table[(2n+1+n^4)n^5/4, {n, 0, 24}]
%t A282614 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 *)
%o A282614 (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
%Y A282614 Cf. A282613, A282614, A217331, A168555. (For 2x2 version see A039623.)
%K A282614 nonn,easy
%O A282614 0,3
%A A282614 _David Nacin_, Feb 19 2017