A292209 - OEIS

%I #11 Feb 16 2025 08:33:51

%S 45,1073,22977,471809,9534465,191475713,3835805697,76766445569,

%T 1535731564545,30717852516353,614382820130817,12287862561046529,

%U 245758900488372225,4915191203906977793,98303929631255822337,1966079437050046578689

%N Number of cliques in the n-Menger sponge graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Clique.html">Clique</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MengerSpongeGraph.html">Menger Sponge Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (29, -188, 160).

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

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

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

%t Table[3 20^n - 2 8^n + 1, {n, 20}]

%t LinearRecurrence[{29, -188, 160}, {45, 1073, 22977}, 20]

%t CoefficientList[Series[(-45 + 232 x - 320 x^2)/(-1 + 29 x - 188 x^2 + 160 x^3), {x, 0, 20}], x]

%K nonn,easy,changed

%O 1,1

%A _Eric W. Weisstein_, Sep 11 2017