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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.
3
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.
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 03 2016
STATUS
approved