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

1,2

Links

Table of n, a(n) for n=1..24.

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).

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).

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]

Prog

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

Crossrefs

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

Sequence in context: A253740 A253733 A241102 * A321115 A253732 A232513

Adjacent sequences: A292542 A292543 A292544 * A292546 A292547 A292548

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 18 2017

Status

approved