A292543 Number of 5-cycles in the n-Sierpinski tetrahedron graph.

0, 96, 384, 1536, 6144, 24576, 98304, 393216, 1572864, 6291456, 25165824, 100663296, 402653184, 1610612736, 6442450944, 25769803776, 103079215104, 412316860416, 1649267441664, 6597069766656, 26388279066624, 105553116266496, 422212465065984, 1688849860263936

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. A002023 (6*4^n).

Cf. A292540 (3-cycles), A292542 (4-cycles), A292545 (6-cycles).

Programs

Mathematica

Table[If[n == 1, 0, 6 4^n], {n, 20}]
Join[{0}, LinearRecurrence[{4}, {96}, 20]]
CoefficientList[Series[96 x/(1 - 4 x), {x, 0, 20}], x]

Formula

a(n) = 6*4^n = A002023(n) for n > 1.

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

G.f.: 96*x^/(1 - 4*x).