A086317 - OEIS

%I #34 Feb 16 2025 08:32:50

%S 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,

%T 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,

%U 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

%N Decimal expansion of asymptotic constant xi for counts of weakly binary trees.

%H Vincenzo Librandi, <a href="/A086317/b086317.txt">Table of n, a(n) for n = 1..1000</a>

%H Lyuben Lichev, Dieter Mitsche, <a href="https://arxiv.org/abs/2007.15574">On the modularity of 3-regular random graphs and random graphs with given degree sequences</a>, arXiv:2007.15574 [math.PR], 2020.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WeaklyBinaryTree.html">Weakly binary tree</a>

%F Equals 1/A240943.

%F Equals lim_{n->infinity} A001190(n)^(1/n). - _Vaclav Kotesovec_, Jul 28 2014

%e 2.48325353617263685856228851817822128918869734...

%t 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 *)

%Y Cf. A001190, A086318, A240943.

%Y Cf. A000672, A003214.

%K nonn,cons,changed

%O 1,1

%A _Eric W. Weisstein_, Jul 15 2003

%E Typos corrected by _Jean-François Alcover_, May 27 2014