cp's OEIS Frontend

A277226 Number of inequivalent (modulo C_4 rotations) square n X n grids with squares coming in two colors and four squares have one of the colors.

%I A277226 #30 Sep 08 2022 08:46:17
%S A277226 1,34,464,3182,14769,53044,158976,416140,980625,2124310,4295376,
%T A277226 8199674,14907809,25992232,43700224,71167704,112680801,173990730,
%U A277226 262690000,388656070,564571601,806527964,1134722304,1574255332,2156041329,2917838014,3905408976,5173826770,6788930625
%N A277226 Number of inequivalent (modulo C_4 rotations) square n X n grids with squares coming in two colors and four squares have one of the colors.
%C A277226 See the k=4 column of table A054772(n, k), with more explanations there.
%H A277226 Colin Barker, <a href="/A277226/b277226.txt">Table of n, a(n) for n = 2..1000</a>
%H A277226 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,2,27,-36,0,36,-27,-2,12,-6,1).
%F A277226 a(n) = A054772(n, 4) = A054772(n, n^2-4), n >= 2.
%F A277226 From _Colin Barker_, Oct 09 2016: (Start)
%F A277226 G.f.: x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5+272*x^6+28*x^7+x^8) / ((1-x)^9*(1+x)^3).
%F A277226 a(n) = (n^8-6*n^6+14*n^4)/96 for n even.
%F A277226 a(n) = (n^8-6*n^6+14*n^4-6*n^2-3)/96 for n odd. (End)
%F A277226 From _Stefan Hollos_, Oct 16 2016: (Start)
%F A277226 a(n) = (C(n^2,4) + C(n^2/2,2) + n^2/2)/4 for n even,
%F A277226 a(n) = (C(n^2,4) + C((n^2-1)/2,2) + (n^2-1)/2)/4 for n odd. (End)
%t A277226 CoefficientList[Series[x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5 +272*x^6+28*x^7+x^8)/((1-x)^9*(1+x)^3), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 22 2018 *)
%o A277226 (PARI) Vec(x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5+272*x^6+28*x^7 +x^8)/((1-x)^9*(1+x)^3) + O(x^40)) \\ _Colin Barker_, Oct 16 2016
%o A277226 (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x^2*(1+28*x+272*x^2+804*x^3+1150*x^4+804*x^5 +272*x^6+28*x^7+x^8)/((1-x)^9*(1+x)^3))); // _G. C. Greubel_, Oct 22 2018
%Y A277226 Cf. A054772, A000012 (k=0), A004652 (k=1), A212714 (k=2), A275799 (k=3).
%K A277226 nonn,easy
%O A277226 2,2
%A A277226 _Wolfdieter Lang_, Oct 06 2016