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

2,2

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).

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)

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A271036 A244495 A107917 * A241633 A302383 A303104

Adjacent sequences: A277223 A277224 A277225 * A277227 A277228 A277229

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 06 2016

Status

approved