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%I #20 Apr 15 2021 11:51:49
%S 0,1,102,2862,34960,252375,1284066,5105212,16912512,48700845,
%T 125512750,295649706,646497072,1328022787,2586463530,4811211000,
%U 8598455296,14835732057,24812155062,40359796390,64032402000
%N Number of inequivalent ways to color a 3 X 3 checkerboard using at most n colors allowing rotations and reflections.
%C Cycle index of symmetry group is (s(1)^9 + s(1)*s(2)^4 + 2*s(1)*s(4)^2 + 4*s(1)^3*s(2)^3)/8.
%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^9 + n^5 + 2*n^3 + 4*n^6)/8.
%F G.f.: x*(38*x^7+1753*x^6+11244*x^5+19535*x^4+10810*x^3+1887*x^2+92*x+1)/(x-1)^10. - _Colin Barker_, Oct 04 2012
%t Table[(n^9+n^5+2*n^3+4*n^6)/8, {n,0,20}]
%Y Row n=3 of A343097.
%Y Cf. A002817 (2 x 2 checkerboard).
%K nonn,easy
%O 0,3
%A _Geoffrey Critzer_, Sep 30 2012