

A333345


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


6



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, 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, 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
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OFFSET

2,5


COMMENTS

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).
Apart from the first digit the same as A176522.  R. J. Mathar, Apr 03 2020


LINKS

Table of n, a(n) for n=2..109.
Clemens Heuberger and Stephan Wagner, The Number of Maximum Matchings in a Tree, Discrete Mathematics, volume 311, issue 21, November 2011, pages 25122542; arXiv preprint, arXiv:1011.6554 [math.CO], 2010.


FORMULA

Equals continued fraction [10; 9] = 10 + 1/(9 + 1/(9 + 1/(9 + 1/...))).  Peter Luschny, Mar 15 2020


EXAMPLE

10.1097722286...


MATHEMATICA

With[{$MaxExtraPrecision = 1000}, First@ RealDigits[(11 + Sqrt[85])/2, 10, 105]] (* Michael De Vlieger, Mar 15 2020 *)


PROG

(PARI) (11 + sqrt(85))/2 \\ Michel Marcus, May 21 2020


CROSSREFS

Sequences growing as this power: A147841, A190872, A333344.
Cf. A333346 (seventh root), A176522.
Sequence in context: A242714 A307715 A269547 * A183699 A203079 A232128
Adjacent sequences: A333342 A333343 A333344 * A333346 A333347 A333348


KEYWORD

cons,nonn


AUTHOR

Kevin Ryde, Mar 15 2020


STATUS

approved



