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A109501 Number of closed walks of length n on the complete graph on 7 nodes from a given node. 10
1, 0, 6, 30, 186, 1110, 6666, 39990, 239946, 1439670, 8638026, 51828150, 310968906, 1865813430, 11194880586, 67169283510, 403015701066, 2418094206390, 14508565238346, 87051391430070, 522308348580426 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Ji Young Choi, A Generalization of Collatz Functions and Jacobsthal Numbers, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.
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
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

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Last modified April 15 11:16 EDT 2024. Contains 371681 sequences. (Running on oeis4.)