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 A190872 #37 Sep 08 2022 08:45:57
%S A190872 0,1,11,112,1133,11455,115808,1170793,11836451,119663824,1209774005,
%T A190872 12230539639,123647969984,1250052813073,12637749213947,
%U A190872 127764766035760,1291672683467837,13058516623824367,132018628710857504,1334678266205013241,13493293269857428115
%N A190872 a(n) = 11*a(n-1) - 9*a(n-2), a(0)=0, a(1)=1.
%C A190872 a(k) is Heuberger and Wagner's G_k at lemma 6.2 (2). They show (theorem 3.3 (1)) that the largest number of maximum matchings in a tree of 7k+1 vertices is a(k+1) and there is a unique free tree with this many maximum matchings. (See A333347 for all tree sizes.) - _Kevin Ryde_, Apr 11 2020
%H A190872 G. C. Greubel, <a href="/A190872/b190872.txt">Table of n, a(n) for n = 0..1000</a>
%H A190872 Clemens Heuberger and Stephan Wagner, <a href="https://doi.org/10.1016/j.disc.2011.07.028">The Number of Maximum Matchings in a Tree</a>, Discrete Mathematics, volume 311, issue 21, November 2011, pages 2512-2542; <a href="https://arxiv.org/abs/1011.6554">arXiv preprint</a>, arXiv:1011.6554 [math.CO], 2010.
%H A190872 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-9).
%F A190872 a(n) = ((11+sqrt(85))^n-(11-sqrt(85))^n)/(2^n*sqrt(85)).
%F A190872 G.f.: x/(1-11*x+9*x^2). - _Philippe Deléham_, Feb 12 2012
%F A190872 E.g.f.: (2/sqrt(85))*exp(11*x/2)*sinh(sqrt(85)*x/2). - _G. C. Greubel_, Dec 18 2015
%F A190872 a(n) = (L^n - H^n)/(L-H) where L = (11+sqrt(85))/2 and H = (11-sqrt(85))/2. [Heuberger and Wagner lemma 6.2 (2)] - _Kevin Ryde_, Apr 11 2020
%t A190872 LinearRecurrence[{11, -9}, {0, 1}, 50] (* _T. D. Noe_, May 23 2011 *)
%o A190872 (PARI) concat(0, Vec(x/(1-11*x+9*x^2) + O(x^100))) \\ _Altug Alkan_, Dec 18 2015
%o A190872 (PARI) a(n) = polcoeff(lift(Mod('x,'x^2-11*'x+9)^n), 1); \\ _Kevin Ryde_, Apr 11 2020
%o A190872 (Magma) I:=[0,1]; [n le 2 select I[n] else 11*Self(n-1)-9*Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Dec 19 2015
%Y A190872 Cf. A333345 (growth power), A190871, A190873.
%K A190872 nonn,easy
%O A190872 0,3
%A A190872 _Rolf Pleisch_, May 22 2011
%E A190872 Extended by _T. D. Noe_, May 23 2011