A289179 Edge count of the n X n white bishop graph.

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

Offset: 1

Author

Eric W. Weisstein, Jun 27 2017

Keywords

• nonn

Comments

Sequence extended to a(1) using formula.

Links

• Eric Weisstein's World of Mathematics, Edge Count
• Eric Weisstein's World of Mathematics, White Bishop Graph
• Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 1, 2, -1).

Crossrefs

Cf. A225972 (black bishop graph edge count).

Programs

Mathematica

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 *)

Formula

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]