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A301459 Number of 6-cycles in the n-folded cube graph. 1
0, 0, 96, 320, 3200, 4480, 14336, 43008, 122880, 337920, 901120, 2342912, 5963776, 14909440, 36700160, 89128960, 213909504, 508035072, 1195376640, 2789212160, 6459228160, 14856224768, 33957085184 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

a(5) is also the number of 6-cycles in the 2-Keller graph.

LINKS

Table of n, a(n) for n=2..24.

Eric Weisstein's World of Mathematics, Folded Cube Graph

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Keller Graph

FORMULA

a(n) = 2^(n - 1)*n*(n - 1)*(n - 2)/3 for n > 6.

a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4) for n > 10.

G.f.: 32*x^4*(3 - 14*x + 92*x^2 - 516*x^3 + 1456*x^4 - 1920*x^5 + 960*x^6)/(-1 + 2*x)^4.

MATHEMATICA

Table[Piecewise[{{0, n == 3}, {96, n == 4}, {3200, n == 6}}, 2^(n - 1) n (n - 1) (n - 2)/3], {n, 2, 20}]

Join[{0, 0, 96, 320, 3200}, LinearRecurrence[{8, -24, 32, -16}, {4480, 14336, 43008, 122880, 337920}, 14]]

CoefficientList[Series[32 x^2 (3 - 14 x + 92 x^2 - 516 x^3 + 1456 x^4 - 1920 x^5 + 960 x^6)/(-1 + 2 x)^4, {x, 0, 20}], x]

CROSSREFS

Cf. A052482 (4-cycles).

Sequence in context: A320883 A048189 A304830 * A220540 A292345 A084048

Adjacent sequences:  A301456 A301457 A301458 * A301460 A301461 A301462

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Mar 21 2018

STATUS

approved

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Last modified July 5 00:40 EDT 2020. Contains 335457 sequences. (Running on oeis4.)