A289864 Number of cliques in the n-triangular honeycomb queen graph.

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

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