This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109501 #32 Aug 21 2024 14:30:07
%S A109501 1,0,6,30,186,1110,6666,39990,239946,1439670,8638026,51828150,
%T A109501 310968906,1865813430,11194880586,67169283510,403015701066,
%U A109501 2418094206390,14508565238346,87051391430070,522308348580426,3133850091482550,18803100548895306,112818603293371830
%N A109501 Number of closed walks of length n on the complete graph on 7 nodes from a given node.
%H A109501 G. C. Greubel, <a href="/A109501/b109501.txt">Table of n, a(n) for n = 0..1000</a>
%H A109501 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 A109501 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 A109501 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,6).
%F A109501 G.f.: (1 - 5*x)/(1 - 5*x - 6*x^2).
%F A109501 a(n) = (6^n + 6*(-1)^n)/7.
%F A109501 a(n) = 6^(n-1) - a(n-1), a(0) = 1. - _Jon E. Schoenfield_, Feb 09 2015
%F A109501 a(n) = 5*a(n-1) + 6*a(n-2). - _G. C. Greubel_, Dec 30 2017
%F A109501 E.g.f.: exp(-x)*(exp(7*x) + 6)/7. - _Elmo R. Oliveira_, Aug 17 2024
%t A109501 k=0;lst={k};Do[k=6^n-k;AppendTo[lst, k], {n, 1, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008 *)
%t A109501 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 *)
%o A109501 (PARI) for(n=0,30, print1((6^n + 6*(-1)^n)/7, ", ")) \\ _G. C. Greubel_, Dec 30 2017
%o A109501 (Magma) [(6^n + 6*(-1)^n)/7: n in [0..30]]; // _G. C. Greubel_, Dec 30 2017
%Y A109501 Cf. A109502.
%Y A109501 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
%K A109501 nonn,easy
%O A109501 0,3
%A A109501 _Mitch Harris_, Jun 30 2005
%E A109501 Corrected by _Franklin T. Adams-Watters_, Sep 18 2006
%E A109501 Edited by _Jon E. Schoenfield_, Feb 09 2015