A292545 Number of 6-cycles in the n-Sierpinski tetrahedron graph.

0, 218, 876, 3504, 14016, 56064, 224256, 897024, 3588096, 14352384, 57409536, 229638144, 918552576, 3674210304, 14696841216, 58787364864, 235149459456, 940597837824, 3762391351296, 15049565405184, 60198261620736, 240793046482944, 963172185931776, 3852688743727104

Offset: 1

Author

Eric W. Weisstein, Sep 18 2017

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Sierpinski Tetrahedron Graph
• Index entries for linear recurrences with constant coefficients, signature (4).

Crossrefs

Cf. A292540 (3-cycles), A292542 (4-cycles), A292543 (5-cycles).

Programs

Mathematica

Table[Piecewise[{{0, n == 1}, {218, n == 2}}, 219 4^(n - 2)], {n, 20}]
Join[{0, 218}, LinearRecurrence[{4}, {876}, 20]]
CoefficientList[Series[-2 x (109 + 2 x)/(-1 + 4 x), {x, 0, 20}], x]

PARI

concat(0, Vec(-2*x^2*(109 + 2*x)/(-1 + 4*x) + O(x^50))) \\ Michel Marcus, Sep 19 2017

Formula

a(n) = 219*4^(n - 2) for n > 2.

a(n) = 4*a(n-1) for n > 2.

G.f.: -2*x^2*(109 + 2*x)/(-1 + 4*x).