A290031 Number of 6-cycles in the n-hypercube graph.

0, 0, 0, 16, 128, 640, 2560, 8960, 28672, 86016, 245760, 675840, 1802240, 4685824, 11927552, 29818880, 73400320, 178257920, 427819008, 1016070144, 2390753280, 5578424320, 12918456320, 29712449536, 67914170368, 154350387200, 348966092800, 785173708800, 1758789107712

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Eric Weisstein's World of Mathematics, Graph Cycle.

Eric Weisstein's World of Mathematics, Hypercube Graph.

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

a(n) = 2^(n + 1)*binomial(n, 3).

a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-4)-16*a(n-4).

G.f.: (16*x^3)/(-1 + 2*x)^4.

From Amiram Eldar, Jan 05 2022: (Start)

Sum_{n>=3} 1/a(n) = 3*(2*log(2)-1)/16.

Sum_{n>=3} (-1)^(n+1)/a(n) = (3/2)^3*log(3/2) - 21/16. (End)

Mathematica

Table[2^(n + 1) Binomial[n, 3], {n, 0, 20}]
LinearRecurrence[{8, -24, 32, -16}, {0, 0, 0, 16}, 20]
CoefficientList[Series[(16 x^3)/(-1 + 2 x)^4, {x, 0, 20}], x]
Table[Length[FindCycle[HypercubeGraph[n], {6}, All]], {n, 0, 10}] (* Eric W. Weisstein, Aug 02 2023 *)

Prog

(Magma) [2^(n + 1)*Binomial(n, 3): n in [0..30]]; // Wesley Ivan Hurt, Apr 21 2021

Crossrefs

Cf. A001788 (4-cycles).

Cf. A364688 (8-cycles).

Sequence in context: A167471 A153115 A138331 * A008535 A008416 A045651

Adjacent sequences: A290028 A290029 A290030 * A290032 A290033 A290034

Keyword

nonn

Author

Eric W. Weisstein, Jul 17 2017

Status

approved