A292209 Number of cliques in the n-Menger sponge graph.

45, 1073, 22977, 471809, 9534465, 191475713, 3835805697, 76766445569, 1535731564545, 30717852516353, 614382820130817, 12287862561046529, 245758900488372225, 4915191203906977793, 98303929631255822337, 1966079437050046578689

Offset

1,1

Links

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, Menger Sponge Graph

Index entries for linear recurrences with constant coefficients, signature (29, -188, 160).

Formula

a(n) = 3*20^n - 2*8^n + 1.

a(n) = 29*a(n-1) - 188*a(n-2) + 160*a(n-3).

G.f.: x*(-45 + 232*x - 320*x^2)/(-1 + 29*x - 188*x^2 + 160*x^3).

Mathematica

Table[3 20^n - 2 8^n + 1, {n, 20}]
LinearRecurrence[{29, -188, 160}, {45, 1073, 22977}, 20]
CoefficientList[Series[(-45 + 232 x - 320 x^2)/(-1 + 29 x - 188 x^2 + 160 x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A162418 A010997 A163721 * A317895 A282929 A177728

Adjacent sequences: A292206 A292207 A292208 * A292210 A292211 A292212

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 11 2017

Status

approved