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

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), A292543 (5-cycles), A292545 (6-cycles).

Programs

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]

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).