A295921 Number of (not necessarily maximal) cliques in the n-folded cube graph.

4, 16, 25, 57, 129, 289, 641, 1409, 3073, 6657, 14337, 30721, 65537, 139265, 294913, 622593, 1310721, 2752513, 5767169, 12058625, 25165825, 52428801, 109051905, 226492417, 469762049, 973078529, 2013265921, 4160749569, 8589934593, 17716740097, 36507222017

Offset

2,1

Links

Table of n, a(n) for n=2..32.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, Folded Cube Graph

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Formula

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

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

G.f.: x^2*(-4 + 4*x + 23*x^2 - 44*x^3 + 20*x^4)/((-1 + x)*(-1 + 2*x)^2).

Mathematica

Table[Piecewise[{{4, n == 2}, {16, n == 3}}, 2^(n - 2) (n + 2) + 1], {n, 2, 20}]
Join[{4, 16}, LinearRecurrence[{5, -8, 4}, {25, 57, 129}, 20]]
CoefficientList[Series[(-4 + 4 x + 23 x^2 - 44 x^3 + 20 x^4)/((-1 + x) (-1 + 2 x)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A075576 A353295 A363428 * A338406 A351979 A111350

Adjacent sequences: A295918 A295919 A295920 * A295922 A295923 A295924

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 30 2017

Status

approved