A109500 Number of closed walks of length n on the complete graph on 6 nodes from a given node.

1, 0, 5, 20, 105, 520, 2605, 13020, 65105, 325520, 1627605, 8138020, 40690105, 203450520, 1017252605, 5086263020, 25431315105, 127156575520, 635782877605, 3178914388020, 15894571940105, 79472859700520

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Ji Young Choi, A Generalization of Collatz Functions and Jacobsthal Numbers, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.

Index entries for linear recurrences with constant coefficients, signature (4,5).

Formula

G.f.: (1 - 4*x)/(1 - 4*x - 5*x^2).

a(n) = (5^n + 5*(-1)^n)/6.

a(n) = 5^(n-1) - a(n-1), a(0) = 1. - Jon E. Schoenfield, Feb 08 2015

Mathematica

k=0; lst={k}; Do[k=5^n-k; AppendTo[lst, k], {n, 1, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
CoefficientList[Series[(1 - 4*x)/(1 - 4*x - 5*x^2), {x, 0, 50}], x] (* or *) Table[(5^n + 5*(-1)^n)/6, {n, 0, 30}] (* G. C. Greubel, Dec 30 2017 *)

Prog

(PARI) for(n=0, 30, print1((5^n + 5*(-1)^n)/6, ", ")) \\ G. C. Greubel, Dec 30 2017
(Magma) [(5^n + 5*(-1)^n)/6: n in [0..30]]; // G. C. Greubel, Dec 30 2017

Crossrefs

Cf. A109502.

Cf. sequences with the same recurrence form: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Sequence in context: A276314 A292358 A259275 * A137961 A334716 A167145

Adjacent sequences: A109497 A109498 A109499 * A109501 A109502 A109503

Keyword

nonn,easy

Author

Mitch Harris, Jun 30 2005

Extensions

Corrected by Franklin T. Adams-Watters, Sep 18 2006

Edited by Jon E. Schoenfield, Feb 08 2015

Status

approved