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A282613 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations.

%I A282613 #17 Apr 15 2021 10:14:03
%S A282613 0,1,140,4995,65824,489125,2521476,10092775,33562880,96870249,
%T A282613 250025500,589527851,1290008160,2651218765,5165397524,9611031375,
%U A282613 17180133376,29647326545,49590297900,80672546899,128000804000,198571037301,301818598180,450289780535
%N A282613 Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations.
%C A282613 Cycle index of symmetry group (cyclic rotation group of order 4 acting on the 9 cells of the square) is (2s(4)^2*s(1) + s(2)^4*s(1) + s(1)^9)/4.
%H A282613 Colin Barker, <a href="/A282613/b282613.txt">Table of n, a(n) for n = 0..1000</a>
%H A282613 <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 A282613 a(n) = n^3*(n^2+1)*(n^4-n^2+2)/4.
%F A282613 G.f.: x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10. - _Colin Barker_, Feb 23 2017
%e A282613 The number of 3 X 3 binary matrices up to rotations is 140.
%t A282613 Table[(2n^3+n^5+n^9)/4, {n, 0, 24}]
%o A282613 (PARI) concat(0, Vec(x*(1 + 130*x + 3640*x^2 + 22054*x^3 + 39070*x^4 + 22054*x^5 + 3640*x^6 + 130*x^7 + x^8) / (1 - x)^10 + O(x^30))) \\ _Colin Barker_, Feb 23 2017
%Y A282613 Row n=3 of A343095.
%Y A282613 Cf. A282612, A282614, A217331, A168555.
%Y A282613 Cf. A006528 (2 x 2 version), A283027 (4 X 4 version).
%K A282613 nonn,easy
%O A282613 0,3
%A A282613 _David Nacin_, Feb 19 2017