A295910 Number of (not necessarily maximal) cliques in the n X n white bishop graph.

4, 9, 30, 61, 160, 301, 718, 1305, 3000, 5377, 12190, 21733, 49024, 87237, 196446, 349345, 786232, 1397881, 3145486, 5592141, 12582624, 22369309, 50331310, 89478121, 201326200, 357913521, 805305918, 1431655285, 3221224960, 5726622517, 12884901310, 22906491633

Offset

2,1

Links

Table of n, a(n) for n=2..33.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, White Bishop Graph

Index entries for linear recurrences with constant coefficients, signature (2, 4, -10, 1, 8, -4).

Formula

a(n) = ((-1)^(n + 1) + 2^(n + 1)*(17 + (-1)^n) - 6*n*(n + 4) - 23)/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.: x^2*(4 + x - 4*x^2 + 5*x^3 + 4*x^4 - 4*x^5)/((-1 + x)^3*(-1 - x + 4*x^2 + 4*x^3)).

Mathematica

Table[((-1)^(n + 1) + 2^(n + 1) (17 + (-1)^n) - 6 n (n + 4) - 23)/12, {n, 20}]
LinearRecurrence[{2, 4, -10, 1, 8, -4}, {4, 9, 30, 61, 160, 301}, 20]
Rest @ CoefficientList[Series[x (4 + x - 4 x^2 + 5 x^3 + 4 x^4 - 4 x^5)/((-1 + x)^3 (-1 - x + 4 x^2 + 4 x^3)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A186650 A091658 A297960 * A086688 A309295 A151270

Adjacent sequences: A295907 A295908 A295909 * A295911 A295912 A295913

Keyword

nonn

Author

Eric W. Weisstein, Nov 29 2017

Status

approved