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A288947 Number of maximal cliques in the n X n queen graph. 0
1, 1, 10, 36, 76, 129, 210, 310, 452, 619, 842, 1096, 1420, 1781, 2226, 2714, 3300, 3935, 4682, 5484, 6412, 7401, 8530, 9726, 11076, 12499, 14090, 15760, 17612, 19549, 21682, 23906, 26340, 28871, 31626, 34484, 37580, 40785, 44242, 47814 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Maximal Clique

Eric Weisstein's World of Mathematics, Queen Graph

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

FORMULA

For n>3, a(n) = n*(73-3*(-1)^n+4*n*(2*n-3))/12-14.

For n>3, a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).

G.f.: -((x^2*(-1+x-7*x^2-19*x^3+3*x^4+22*x^5-9*x^6-10*x^7+4*x^8))/((-1+x)^4*(1+x)^2)).

MATHEMATICA

Table[Piecewise[{{1, n < 3}, {10, n == 3}}, n (73 - 3 (-1)^n + 4 n (2 n - 3))/12 - 14], {n, 20}]

Join[{1, 1}, LinearRecurrence[{2, 1, -4, 1, 2, -1}, {-28, -9, 10, 36, 76, 129}, {3, 20}]]

CoefficientList[Series[(1 - x + 7 x^2 + 19 x^3 - 3 x^4 - 22 x^5 + 9 x^6 + 10 x^7 - 4 x^8)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A309783 A072517 A271912 * A328146 A033585 A118629

Adjacent sequences:  A288944 A288945 A288946 * A288948 A288949 A288950

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jun 20 2017

STATUS

approved

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)