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%I #23 Oct 17 2016 03:50:21
%S 1,22,140,578,1785,4612,10416,21340,40425,72010,121836,197582,308945,
%T 468328,690880,995352,1404081,1944030,2646700,3549370,4694921,6133292,
%U 7921200,10123828,12814425,16076242,20001996,24696070,30273825,36864080
%N Number of inequivalent (modulo C_4 rotations) square n X n grids with squares coming in two colors and three squares have one of the colors.
%C See the k=3 column of table A054772(n, k), with more explanations there.
%H Colin Barker, <a href="/A275799/b275799.txt">Table of n, a(n) for n = 2..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-8,14,0,-14,8,3,-4,1).
%F a(n) = A054772(n, 3) = A054772(n, n^2-3), n >= 2.
%F From _Colin Barker_, Oct 09 2016: (Start)
%F G.f.: x^2*(1+18*x+55*x^2+92*x^3+55*x^4+18*x^5+x^6) / ((1-x)^7*(1+x)^3).
%F a(n) = (n^6-3*n^4+2*n^2)/24 for n even.
%F a(n) = (n^6-3*n^4+5*n^2-3)/24 for n odd. (End)
%F From _Stefan Hollos_, Oct 16 2016: (Start)
%F a(n) = C(n^2,3)/4 for n even,
%F a(n) = (C(n^2,3) + (n^2-1)/2)/4 for n odd. (End)
%o (PARI) Vec(x^2*(1+18*x+55*x^2+92*x^3+55*x^4+18*x^5+x^6)/((1-x)^7*(1+x)^3) + O(x^40)) \\ _Colin Barker_, Oct 16 2016
%Y Cf. A054772, A000012 (k=0), A004652 (k=1), A212714 (k=2).
%K nonn,easy
%O 2,2
%A _Wolfdieter Lang_, Oct 03 2016