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A289179
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Edge count of the n X n white bishop graph.
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1
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0, 1, 4, 14, 28, 55, 88, 140, 200, 285, 380, 506, 644, 819, 1008, 1240, 1488, 1785, 2100, 2470, 2860, 3311, 3784, 4324, 4888, 5525, 6188, 6930, 7700, 8555, 9440, 10416, 11424, 12529, 13668, 14910, 16188, 17575, 19000, 20540, 22120, 23821, 25564, 27434, 29348, 31395
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OFFSET
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1,3
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COMMENTS
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Sequence extended to a(1) using formula.
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LINKS
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FORMULA
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a(n) = ((-1 + n)*(-3 + 3*(-1)^n - 2*n + 4*n^2))/12.
a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
G.f. = x*(x + 2x^2 + 5x^3)/((-1 + x)^4*(1 + x)^2). [Corrected by Georg Fischer, May 19 2019]
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MATHEMATICA
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Table[(n - 1) (4 n^2 - 2 n - 3 + 3 (-1)^n)/12, {n, 20}]
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 4, 14, 28, 55}, 20]
CoefficientList[Series[x(x + 2 x^2+ 5 x^3)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x] (* Corrected by Georg Fischer, May 19 2019 *)
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CROSSREFS
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Cf. A225972 (black bishop graph edge count).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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