A086317 Decimal expansion of asymptotic constant xi for counts of weakly binary trees.
2, 4, 8, 3, 2, 5, 3, 5, 3, 6, 1, 7, 2, 6, 3, 6, 8, 5, 8, 5, 6, 2, 2, 8, 8, 5, 1, 8, 1, 7, 8, 2, 2, 1, 2, 8, 9, 1, 8, 8, 6, 9, 7, 3, 4, 0, 8, 1, 4, 3, 6, 4, 5, 8, 5, 9, 2, 0, 2, 5, 9, 6, 9, 7, 3, 0, 6, 7, 4, 2, 5, 4, 0, 8, 8, 5, 8, 0, 9, 8, 3, 9, 0, 6, 4, 7, 6, 4, 0, 1, 6, 9, 1, 6, 7, 2, 1, 8, 2, 7, 4, 7
Offset: 1
Examples
2.48325353617263685856228851817822128918869734...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Lyuben Lichev, Dieter Mitsche, On the modularity of 3-regular random graphs and random graphs with given degree sequences, arXiv:2007.15574 [math.PR], 2020.
- Eric Weisstein's World of Mathematics, Weakly binary tree
Programs
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Mathematica
digits = 102; c[0] = 2; c[n_] := c[n] = c[n - 1]^2 + 2; xi[n_Integer] := xi[n] = c[n]^(2^-n); xi[5]; xi[n = 10]; While[RealDigits[xi[n], 10, digits] != RealDigits[xi[n - 5], 10, digits], n = n + 5]; RealDigits[xi[n], 10, digits] // First (* Jean-François Alcover, May 27 2014 *)
Formula
Equals 1/A240943.
Equals lim_{n->infinity} A001190(n)^(1/n). - Vaclav Kotesovec, Jul 28 2014
Extensions
Typos corrected by Jean-François Alcover, May 27 2014