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A292540
Number of 3-cycles in the n-Sierpinski tetrahedron graph.
3
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
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Sierpinski Tetrahedron Graph
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. A292542 (4-cycles), A292543 (5-cycles), A292545 (6-cycles).
Sequence in context: A074358 A255050 A371408 * A320934 A344063 A055296
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 18 2017
STATUS
approved