A109500 - OEIS

%I #28 May 30 2024 00:36:44

%S 1,0,5,20,105,520,2605,13020,65105,325520,1627605,8138020,40690105,

%T 203450520,1017252605,5086263020,25431315105,127156575520,

%U 635782877605,3178914388020,15894571940105,79472859700520

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

%H G. C. Greubel, <a href="/A109500/b109500.txt">Table of n, a(n) for n = 0..1000</a>

%H Ji Young Choi, <a href="https://www.emis.de/journals/JIS/VOL21/Choi/choi10.html">A Generalization of Collatz Functions and Jacobsthal Numbers</a>, J. Int. Seq., Vol. 21 (2018), Article 18.5.4.

%H Christopher R. Kitching, Henri Kauhanen, Jordan Abbott, Deepthi Gopal, Ricardo Bermúdez-Otero, and Tobias Galla, <a href="https://arxiv.org/abs/2405.12023">Estimating transmission noise on networks from stationary local order</a>, arXiv:2405.12023 [cond-mat.stat-mech], 2024. See p. 48.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,5).

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

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

%F a(n) = 5^(n-1) - a(n-1), a(0) = 1. - _Jon E. Schoenfield_, Feb 08 2015

%t k=0;lst={k};Do[k=5^n-k;AppendTo[lst, k], {n, 1, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008 *)

%t 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 *)

%o (PARI) for(n=0, 30, print1((5^n + 5*(-1)^n)/6, ", ")) \\ _G. C. Greubel_, Dec 30 2017

%o (Magma) [(5^n + 5*(-1)^n)/6: n in [0..30]]; // _G. C. Greubel_, Dec 30 2017

%Y Cf. A109502.

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

%K nonn,easy

%O 0,3

%A _Mitch Harris_, Jun 30 2005

%E Corrected by _Franklin T. Adams-Watters_, Sep 18 2006

%E Edited by _Jon E. Schoenfield_, Feb 08 2015