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Decimal expansion of ((11 + sqrt(85))/2)^(1/7).
2

%I #16 Apr 01 2020 15:39:15

%S 1,3,9,1,6,6,4,2,8,4,1,3,9,8,8,8,5,1,0,5,7,4,5,8,1,2,3,8,4,5,7,9,3,3,

%T 0,0,9,0,0,6,0,3,5,6,6,5,7,0,0,4,5,5,0,6,8,8,8,0,1,4,7,8,4,9,7,8,4,7,

%U 4,8,0,0,4,5,3,6,8,8,9,1,0,1,1,9,9,6,9,2,2,8,1,0,2,9,6,1,6,1,4,6,8,4,7,8,3,0,5,4

%N Decimal expansion of ((11 + sqrt(85))/2)^(1/7).

%C Heuberger and Wagner consider the number of maximum matchings a tree of n vertices may have. They show that the largest number of maximum matchings (A333347) grows as O(1.3916...^n) where the power is the constant here. This arises in their tree forms since each 7-vertex "C" part increases the number of matchings by a factor of matrix M=[8,3/5,3] (lemma 6.2). The larger eigenvalue of M is their lambda = A333345 and so a factor of lambda for each 7 vertices.

%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.

%e 1.39166428413...

%t RealDigits[((11 + Sqrt[85])/2)^(1/7), 10, 100][[1]] (* _Amiram Eldar_, Mar 15 2020 *)

%Y Sequence growing as this power: A333347.

%K nonn,cons

%O 1,2

%A _Kevin Ryde_, Mar 15 2020