A333345 Decimal expansion of (11 + sqrt(85))/2.

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

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 2512-2542; 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