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%I #32 May 21 2020 07:08:09
%S 1,0,1,0,9,7,7,2,2,2,8,6,4,6,4,4,3,6,5,5,0,0,1,1,3,7,1,4,0,8,8,1,3,9,
%T 6,5,7,8,6,2,3,4,0,2,5,2,4,3,6,1,2,3,2,0,0,4,0,0,3,8,7,6,1,0,2,7,2,1,
%U 3,3,5,5,1,3,4,0,0,9,3,7,7,3,0,3,8,3,9,4,7,0,4,5,3,9,6,6,4,0,2,8,2,4,7,0,1,6,9,9
%N Decimal expansion of (11 + sqrt(85))/2.
%C This constant is Heuberger and Wagner's lambda. They consider the number of maximum matchings a tree of n vertices may have, and show that the largest number of maximum matchings (A333347) grows as O(lambda^(n/7)) (see A333346 for the 7th root). Lambda is the larger eigenvalue of matrix M = [8,3/5,3] which is raised to a power when counting matchings in a chain of "C" parts in the trees (their lemma 6.2).
%C Apart from the first digit the same as A176522. - _R. J. Mathar_, Apr 03 2020
%H 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.
%F Equals continued fraction [10; 9] = 10 + 1/(9 + 1/(9 + 1/(9 + 1/...))). - _Peter Luschny_, Mar 15 2020
%e 10.1097722286...
%t With[{$MaxExtraPrecision = 1000}, First@ RealDigits[(11 + Sqrt[85])/2, 10, 105]] (* _Michael De Vlieger_, Mar 15 2020 *)
%o (PARI) (11 + sqrt(85))/2 \\ _Michel Marcus_, May 21 2020
%Y Sequences growing as this power: A147841, A190872, A333344.
%Y Cf. A333346 (seventh root), A176522.
%K cons,nonn
%O 2,5
%A _Kevin Ryde_, Mar 15 2020
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