A289877 Number of maximal cliques in the n-triangular honeycomb queen graph.

1, 8, 19, 36, 60, 93, 136, 191, 259, 342, 441, 558, 694, 851, 1030, 1233, 1461, 1716, 1999, 2312, 2656, 3033, 3444, 3891, 4375, 4898, 5461, 6066, 6714, 7407, 8146, 8933, 9769, 10656, 11595, 12588, 13636, 14741, 15904, 17127

Offset

2,2

Comments

Using the formula to extend to a(1) gives -3, while the 1-triangular honeycomb grid graph has 1 maximal clique.

Links

Table of n, a(n) for n=2..41.

Eric Weisstein's World of Mathematics, Maximal Clique

Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Formula

a(n) = (2*n*(22 - n + 2*n^2) - 95 - (-1)^n)/16.

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

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

Mathematica

Table[(2 n (22 - n + 2 n^2) - 95 - (-1)^n)/16, {n, 2, 20}]
LinearRecurrence[{3, -2, -2, 3, -1}, {1, 8, 19, 36, 60, 93}, 20]
CoefficientList[Series[(1 + 5 x - 3 x^2 - 3 x^3 + 3 x^4)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x]

Prog

(PARI) a(n)=(2*n*(2*n^2-n+22)-95+1)>>4 \\ Charles R Greathouse IV, Jul 14 2017

Crossrefs

Sequence in context: A135027 A158916 A045557 * A089111 A127873 A192975

Adjacent sequences: A289874 A289875 A289876 * A289878 A289879 A289880

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 14 2017

Status

approved