A333346 Decimal expansion of ((11 + sqrt(85))/2)^(1/7).

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, 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, 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

Offset: 1

Author

Kevin Ryde, Mar 15 2020

Keywords

• nonn
• cons

Comments

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.

Examples

			1.39166428413...
		

Links

• 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.

Crossrefs

Sequence growing as this power: A333347.

Cf. A333345.

Programs

Mathematica

RealDigits[((11 + Sqrt[85])/2)^(1/7), 10, 100][[1]] (* Amiram Eldar, Mar 15 2020 *)

PARI

((11 + sqrt(85))/2)^(1/7) \\ Stefano Spezia, Feb 09 2025