A295922 Number of (not necessarily maximal) cliques in the n-halved cube graph.

2, 4, 16, 81, 393, 1777, 7633, 31745, 129537, 523009, 2099969, 8409089, 33634305, 134475777, 537628673, 2149580801, 8595505153, 34374090753, 137475063809, 549844942849, 2199239786497, 8796612067329, 35185602068481, 140740374036481, 562956664307713

Offset

1,1

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Clique

Eric Weisstein's World of Mathematics, Halved Cube Graph

Index entries for linear recurrences with constant coefficients, signature (13, -68, 184, -272, 208, -64).

Formula

a(n) = (24*(2 + 4^n) + 2^n*n*((n - 9)*n - 16))/48.

a(n) = 13*a(n-1) - 68*a(n-2) + 184*a(n-3) - 272*a(n-4) + 208*a(n-5) - 64*a(n-6).

G.f.: x (2 - 22*x + 100*x^2 - 223*x^3 + 236*x^4 - 96*x^5)/((-1 + 2*x)^4*(1 - 5*x + 4*x^2)).

Mathematica

Table[(24 (2 + 4^n) + 2^n n ((n - 9) n - 16))/48, {n, 20}]
LinearRecurrence[{13, -68, 184, -272, 208, -64}, {2, 4, 16, 81, 393, 1777}, 20]
CoefficientList[Series[(2 - 22 x + 100 x^2 - 223 x^3 + 236 x^4 - 96 x^5)/((-1 + 2 x)^4 (1 - 5 x + 4 x^2)), {x, 0, 20}], x]

Prog

(PARI) a(n)=(24*4^n+2^n*n*(n*(n-9)-16))/48+1 \\ Charles R Greathouse IV, Nov 30 2017

Crossrefs

Sequence in context: A213010 A000831 A000090 * A300100 A212432 A351287

Adjacent sequences: A295919 A295920 A295921 * A295923 A295924 A295925

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 30 2017

Status

approved