A288947 Number of maximal cliques in the n X n queen graph.

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

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