A275799 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.

1, 22, 140, 578, 1785, 4612, 10416, 21340, 40425, 72010, 121836, 197582, 308945, 468328, 690880, 995352, 1404081, 1944030, 2646700, 3549370, 4694921, 6133292, 7921200, 10123828, 12814425, 16076242, 20001996, 24696070, 30273825, 36864080

Offset

2,2

Comments

See the k=3 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 (4,-3,-8,14,0,-14,8,3,-4,1).

Formula

a(n) = A054772(n, 3) = A054772(n, n^2-3), n >= 2.

From Colin Barker, Oct 09 2016: (Start)

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).

a(n) = (n^6-3*n^4+2*n^2)/24 for n even.

a(n) = (n^6-3*n^4+5*n^2-3)/24 for n odd. (End)

From Stefan Hollos, Oct 16 2016: (Start)

a(n) = C(n^2,3)/4 for n even,

a(n) = (C(n^2,3) + (n^2-1)/2)/4 for n odd. (End)

Prog

(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

Crossrefs

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

Sequence in context: A183909 A263481 A238170 * A185397 A179792 A125332

Adjacent sequences: A275796 A275797 A275798 * A275800 A275801 A275802

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 03 2016

Status

approved