A301459 Number of 6-cycles in the n-folded cube graph.

0, 0, 96, 320, 3200, 4480, 14336, 43008, 122880, 337920, 901120, 2342912, 5963776, 14909440, 36700160, 89128960, 213909504, 508035072, 1195376640, 2789212160, 6459228160, 14856224768, 33957085184, 77175193600, 174483046400, 392586854400, 879394553856, 1961726312448

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..29.

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.

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

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.

From Amiram Eldar, Sep 28 2025: (Start)

Sum_{n>=4} 1/a(n) = 3*log(2)/4 - 9709/19200.

Sum_{n>=4} (-1)^n/a(n) = 52691/19200 - 27*log(3/2)/4. (End)

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