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.

1, 34, 464, 3182, 14769, 53044, 158976, 416140, 980625, 2124310, 4295376, 8199674, 14907809, 25992232, 43700224, 71167704, 112680801, 173990730, 262690000, 388656070, 564571601, 806527964, 1134722304, 1574255332, 2156041329, 2917838014, 3905408976, 5173826770, 6788930625

Offset: 2

Author

Wolfdieter Lang, Oct 06 2016

Keywords

• nonn
• easy

Comments

See the k=4 column of table A054772(n, k), with more explanations there.

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-12,2,27,-36,0,36,-27,-2,12,-6,1).

Crossrefs

Cf. A054772, A000012 (k=0), A004652 (k=1), A212714 (k=2), A275799 (k=3).

Programs

Magma

m:=50; R:=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

Mathematica

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 *)

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

Formula

a(n) = A054772(n, 4) = A054772(n, n^2-4), n >= 2.

From Colin Barker, Oct 09 2016: (Start)

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).

a(n) = (n^8-6*n^6+14*n^4)/96 for n even.

a(n) = (n^8-6*n^6+14*n^4-6*n^2-3)/96 for n odd. (End)

From Stefan Hollos, Oct 16 2016: (Start)

a(n) = (C(n^2,4) + C(n^2/2,2) + n^2/2)/4 for n even,

a(n) = (C(n^2,4) + C((n^2-1)/2,2) + (n^2-1)/2)/4 for n odd. (End)