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A289864 Number of cliques in the n-triangular honeycomb queen graph. 0
2, 8, 27, 72, 169, 367, 764, 1553, 3120, 6234, 12433, 24790, 49451, 98705, 197130, 393879, 787258, 1573876, 3146951, 6292916, 12584637, 25167843, 50333992, 100665997, 201329684, 402656702, 805310349, 1610617218, 3221230495, 6442456549, 12884908118, 25769810675 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Here, cliques means any complete subgraph (not just of maximum size).

LINKS

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Clique

Index entries for linear recurrences with constant coefficients, signature (5, -8, 2, 7, -7, 2).

FORMULA

a(n) = (4*n^3 - 18*n^2 - 68*n - 79 - (-1)^n + 3*2^(n + 5))/16.

a(n) = 5*a(n-10-8*a(n-2)+2*a(n-3)+7*a(n-4)-7*a(n-5)+2*a(n-6).

G.f.: (x*(-2 + 2*x - 3*x^2 + 3*x^3 + 5*x^4 - 2*x^5))/((-1 + x)^4*(-1 + x + 2*x^2)).

MATHEMATICA

Table[(4 n^3 - 18 n^2 - 68 n - 79 - (-1)^n + 3 2^(n + 5))/16, {n, 20}]

LinearRecurrence[{5, -8, 2, 7, -7, 2}, {2, 8, 27, 72, 169, 367}, 20]

CoefficientList[Series[(-2 + 2 x - 3 x^2 + 3 x^3 + 5 x^4 - 2 x^5)/((-1 + x)^4 (-1 + x + 2 x^2)), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A347595 A184628 A092071 * A290056 A100505 A102759

Adjacent sequences:  A289861 A289862 A289863 * A289865 A289866 A289867

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jul 13 2017

STATUS

approved

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Last modified December 7 22:50 EST 2021. Contains 349590 sequences. (Running on oeis4.)