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A290031 Number of 6-cycles in the n-hypercube graph. 1
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 (list; graph; refs; listen; history; text; internal format)
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.

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]

PROG

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

CROSSREFS

Cf. A001788 (4-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

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Last modified October 23 08:40 EDT 2021. Contains 348211 sequences. (Running on oeis4.)