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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, 3133850091482550, 18803100548895306, 112818603293371830
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.
Christopher R. Kitching, Henri Kauhanen, Jordan Abbott, Deepthi Gopal, Ricardo Bermúdez-Otero, and Tobias Galla, Estimating transmission noise on networks from stationary local order, arXiv:2405.12023 [cond-mat.stat-mech], 2024. See p. 48.
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
E.g.f.: exp(-x)*(exp(7*x) + 6)/7. - Elmo R. Oliveira, Aug 17 2024
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