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

Offset: 2

Author

Eric W. Weisstein, Mar 21 2018

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

Cf. A052482 (4-cycles).

Programs

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]

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.