A292542 Number of 4-cycles in the n-Sierpinski tetrahedron graph.

3, 39, 156, 624, 2496, 9984, 39936, 159744, 638976, 2555904, 10223616, 40894464, 163577856, 654311424, 2617245696, 10468982784, 41875931136, 167503724544, 670014898176, 2680059592704, 10720238370816, 42880953483264, 171523813933056, 686095255732224

Offset

1,1

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) = 39*4^(n - 2) for n > 1.

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

G.f.: -3*x*(1 + 9*x)/(-1 + 4*x).

Mathematica

Table[If[n == 1, 3, 39 4^(n - 1)], {n, 30}]
Join[{3}, LinearRecurrence[{4}, {39}, 20]]
CoefficientList[Series[-3 (1 + 9 x)/(-1 + 4 x), {x, 0, 20}], x]

Crossrefs

Cf. A292540 (3-cycles), A292543 (5-cycles), A292545 (6-cycles).

Sequence in context: A153875 A082954 A209366 * A212664 A342969 A050392

Adjacent sequences: A292539 A292540 A292541 * A292543 A292544 A292545

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 18 2017

Status

approved