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A295910
Number of (not necessarily maximal) cliques in the n X n white bishop graph.
1
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
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, White Bishop Graph
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Nov 29 2017
STATUS
approved