A295932 Number of (not necessarily maximal) cliques in the n-Sierpinski carpet graph.

17, 153, 1289, 10521, 84809, 680409, 5449097, 43610265, 348934601, 2791634265, 22333546505, 178669789209, 1429362565193, 11434913276121, 91479344472713, 731834870572953, 5854679308957385, 46837435504780377, 374699487137606921, 2997595906398947097, 23980767279085851977

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph

Index entries for linear recurrences with constant coefficients, signature (12, -35, 24).

Formula

a(n) = (13*8^n - 8*3^n + 5)/5.

a(n) = 12*a(n-1) - 35*a(n-2) + 24*a(n-3).

G.f.: x*(-17 + 51*x - 48*x^2)/(-1 + 12*x - 35*x^2 + 24*x^3).

Mathematica

Table[(13 8^n - 8 3^n + 5)/5, {n, 10}]
LinearRecurrence[{12, -35, 24}, {17, 153, 1289}, 20]
CoefficientList[Series[(-17 + 51 x - 48 x^2)/(-1 + 12 x - 35 x^2 + 24 x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A010969 A022582 A164543 * A298458 A160699 A034272

Adjacent sequences: A295929 A295930 A295931 * A295933 A295934 A295935

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 29 2017

Status

approved