Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Apr 15 2021 10:14:03
%S 0,1,140,4995,65824,489125,2521476,10092775,33562880,96870249,
%T 250025500,589527851,1290008160,2651218765,5165397524,9611031375,
%U 17180133376,29647326545,49590297900,80672546899,128000804000,198571037301,301818598180,450289780535
%N Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to rotations.
%C 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 Colin Barker, <a href="/A282613/b282613.txt">Table of n, a(n) for n = 0..1000</a>
%H <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 a(n) = n^3*(n^2+1)*(n^4-n^2+2)/4.
%F 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 The number of 3 X 3 binary matrices up to rotations is 140.
%t Table[(2n^3+n^5+n^9)/4, {n, 0, 24}]
%o (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 Row n=3 of A343095.
%Y Cf. A282612, A282614, A217331, A168555.
%Y Cf. A006528 (2 x 2 version), A283027 (4 X 4 version).
%K nonn,easy
%O 0,3
%A _David Nacin_, Feb 19 2017