A292000 Number of (undirected) paths in the n-gear graph.

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

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