This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A333346 #19 Feb 09 2025 16:07:23 %S A333346 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 A333346 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 A333346 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 A333346 Decimal expansion of ((11 + sqrt(85))/2)^(1/7). %C A333346 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 A333346 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 A333346 1.39166428413... %t A333346 RealDigits[((11 + Sqrt[85])/2)^(1/7), 10, 100][[1]] (* _Amiram Eldar_, Mar 15 2020 *) %o A333346 (PARI) ((11 + sqrt(85))/2)^(1/7) \\ _Stefano Spezia_, Feb 09 2025 %Y A333346 Sequence growing as this power: A333347. %Y A333346 Cf. A333345. %K A333346 nonn,cons %O A333346 1,2 %A A333346 _Kevin Ryde_, Mar 15 2020