login
A295909
Number of (not necessarily maximal) cliques in the n X n black bishop graph.
1
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
Eric Weisstein's World of Mathematics, Black Bishop Graph
Eric Weisstein's World of Mathematics, Clique
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: A372941 A263987 A333710 * A347701 A095977 A129744
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Nov 29 2017
STATUS
approved