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 A292000 Number of (undirected) paths in the n-gear graph. 0
 5, 33, 117, 322, 745, 1515, 2793, 4772, 7677, 11765, 17325, 24678, 34177, 46207, 61185, 79560, 101813, 128457, 160037, 197130, 240345, 290323, 347737, 413292, 487725, 571805, 666333, 772142, 890097, 1021095, 1166065, 1325968, 1501797, 1694577, 1905365, 2135250 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Extended to a(1)-a(2) using the formula/recurrence. LINKS Table of n, a(n) for n=1..36. Eric Weisstein's World of Mathematics, Gear Graph Eric Weisstein's World of Mathematics, Graph Path Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA a(n) = n*(-21 + 58*n - 15*n^2 + 8*n^3)/6. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). G.f.: x*(-5 - 8*x - 2*x^2 - 17*x^3)/(-1 + x)^5. MATHEMATICA Table[n (-21 + 58 n - 15 n^2 + 8 n^3)/6, {n, 20}] LinearRecurrence[{5, -10, 10, -5, 1}, {5, 33, 117, 322, 745}, 20] CoefficientList[Series[(-5 - 8 x - 2 x^2 - 17 x^3)/(-1 + x)^5, {x, 0, 20}], x] CROSSREFS Sequence in context: A250273 A050830 A211059 * A146263 A359703 A255943 Adjacent sequences: A291997 A291998 A291999 * A292001 A292002 A292003 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Sep 07 2017 STATUS approved

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Last modified May 30 06:53 EDT 2023. Contains 363045 sequences. (Running on oeis4.)