%I #9 May 19 2019 15:55:08

%S 0,1,4,14,28,55,88,140,200,285,380,506,644,819,1008,1240,1488,1785,

%T 2100,2470,2860,3311,3784,4324,4888,5525,6188,6930,7700,8555,9440,

%U 10416,11424,12529,13668,14910,16188,17575,19000,20540,22120,23821,25564,27434,29348,31395

%N Edge count of the n X n white bishop graph.

%C Sequence extended to a(1) using formula.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EdgeCount.html">Edge Count</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WhiteBishopGraph.html">White Bishop Graph</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).

%F a(n) = ((-1 + n)*(-3 + 3*(-1)^n - 2*n + 4*n^2))/12.

%F a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).

%F G.f. = x*(x + 2x^2 + 5x^3)/((-1 + x)^4*(1 + x)^2). [Corrected by _Georg Fischer_, May 19 2019]

%t Table[(n - 1) (4 n^2 - 2 n - 3 + 3 (-1)^n)/12, {n, 20}]

%t LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 4, 14, 28, 55}, 20]

%t 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 *)

%Y Cf. A225972 (black bishop graph edge count).

%K nonn

%O 1,3

%A _Eric W. Weisstein_, Jun 27 2017