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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 07:34 EDT 2024. Contains 375842 sequences. (Running on oeis4.)