A109501 Number of closed walks of length n on the complete graph on 7 nodes from a given node.

1, 0, 6, 30, 186, 1110, 6666, 39990, 239946, 1439670, 8638026, 51828150, 310968906, 1865813430, 11194880586, 67169283510, 403015701066, 2418094206390, 14508565238346, 87051391430070, 522308348580426

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 (5,6).

Formula

G.f.: (1 - 5*x)/(1 - 5*x - 6*x^2).

a(n) = (6^n + 6*(-1)^n)/7.

a(n) = 6^(n-1) - a(n-1), a(0) = 1. - Jon E. Schoenfield, Feb 09 2015

a(n) = 5*a(n-1) + 6*a(n-2). - G. C. Greubel, Dec 30 2017

Mathematica

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

Prog

(PARI) for(n=0, 30, print1((6^n + 6*(-1)^n)/7, ", ")) \\ G. C. Greubel, Dec 30 2017
(Magma) [(6^n + 6*(-1)^n)/7: 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, A109500, A015540. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Sequence in context: A357599 A368524 A259276 * A239488 A147517 A294221

Adjacent sequences: A109498 A109499 A109500 * A109502 A109503 A109504

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 09 2015

Status

approved