%I #14 Dec 28 2022 10:37:14

%S 69,161,401,961,2241,5121,11521,25601,56321,122881,266241,573441,

%T 1228801,2621441,5570561,11796481,24903681,52428801,110100481,

%U 230686721,482344961,1006632961,2097152001,4362076161,9059696641,18790481921,38923141121,80530636801,166429982721

%N Number of (not necessarily maximal) cliques in the n-cube-connected cycle graph.

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cube-ConnectedCycleGraph.html">Cube-Connected Cycle Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, -8, 4).

%F a(n) = 5*2^(n - 1)*n + 1 for n > 3.

%F a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) for n > 3.

%F G.f.: x^3*(-69 + 184*x - 148*x^2 + 32*x^3)/((-1 + x)*(-1 + 2*x)^2).

%t Table[If[n == 3, 69, 5 2^(n - 1) n + 1], {n, 3, 20}]

%t Join[{69}, LinearRecurrence[{5, -8, 4}, {161, 401, 961}, 20]]

%t CoefficientList[Series[(-69 + 184 x - 148 x^2 + 32 x^3)/((-1 + x) (-1 + 2 x)^2), {x, 0, 20}], x]

%K nonn

%O 3,1

%A _Eric W. Weisstein_, Nov 29 2017