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

1,1

Links

Table of n, a(n) for n=1..32.

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).

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)).

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]

Crossrefs

Sequence in context: A304341 A263987 A333710 * A347701 A095977 A129744

Adjacent sequences: A295906 A295907 A295908 * A295910 A295911 A295912

Keyword

nonn

Author

Eric W. Weisstein, Nov 29 2017

Status

approved