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

Author

Eric W. Weisstein, Nov 29 2017

Keywords

• nonn

Links

• 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).

Programs

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]

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)).