A292540 Number of 3-cycles in the n-Sierpinski tetrahedron graph.

4, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709120, 21474836480, 85899345920, 343597383680, 1374389534720, 5497558138880, 21990232555520, 87960930222080, 351843720888320, 1407374883553280

Offset

1,1

Links

Table of n, a(n) for n=1..25.

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) = 5*4^(n - 1) for n > 1.

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

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

Mathematica

Table[If[n == 1, 4, 5 4^(n - 1)], {n, 10}]
Join[{4}, LinearRecurrence[{4}, {20}, 30]]
CoefficientList[Series[-((4 (1 + x))/(-1 + 4 x)), {x, 0, 20}], x]
Join[{4}, NestList[4#&, 20, 30]] (* Harvey P. Dale, Sep 21 2019 *)

Crossrefs

Cf. A003947, A269696.

Cf. A292542 (4-cycles), A292543 (5-cycles), A292545 (6-cycles).

Sequence in context: A074358 A255050 A371408 * A320934 A344063 A055296

Adjacent sequences: A292537 A292538 A292539 * A292541 A292542 A292543

Keyword

nonn

Author

Eric W. Weisstein, Sep 18 2017

Status

approved