A295909 Number of (not necessarily maximal) cliques in the n X n black bishop graph.

2, 4, 14, 30, 82, 160, 386, 718, 1646, 3000, 6742, 12190, 27194, 49024, 109082, 196446, 436726, 786232, 1747406, 3145486, 6990242, 12582624, 27961714, 50331310, 111847742, 201326200, 447392006, 805305918, 1789569226, 3221224960, 7158278282, 12884901310

Offset: 1

Author

Eric W. Weisstein, Nov 29 2017

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Black Bishop Graph
• Eric Weisstein's World of Mathematics, Clique
• Index entries for linear recurrences with constant coefficients, signature (2, 4, -10, 1, 8, -4).

Programs

Mathematica

Table[((-2)^(n + 1) + (-1)^n + 19 2^(n + 1) - 6 n (n + 4) - 25)/12, {n, 20}]
LinearRecurrence[{2, 4, -10, 1, 8, -4}, {2, 4, 14, 30, 82, 160}, 20]
CoefficientList[Series[-2 (-1 + x^2 - 3 x^3 - 2 x^4 + 2 x^5)/((-1 + x)^3 (-1 - x + 4 x^2 + 4 x^3)), {x, 0, 20}], x]

Formula

a(n) = ((-2)^(n + 1) + (-1)^n + 19*2^(n + 1) - 6*n*(n + 4) - 25)/12.

a(n) = 2*a(n-1) + 4*a(n-2) - 10*a(n-3) + a(n-4) + 8*a(n-5) - 4*a(n-6).

G.f.: -2*x*(-1 + x^2 - 3*x^3 - 2*x^4 + 2*x^5)/((-1 + x)^3 (-1 - x + 4*x^2 + 4*x^3)).