login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Decimal expansion of a coefficient associated with the asymptotics of the variance of the distance between a vertex and the root of a random rooted tree.
1

%I #7 Mar 07 2023 10:23:05

%S 3,5,2,9,6,2,2,2,2,9,0,5,8,7,7,1,1,1,6,0,8,0,3,4,8,7,4,4,0,4,9,9,6,1,

%T 2,9,2,9,2,7,5,2,5,3,9,5,3,0,6,2,3,2,2,3,3,8,9,5,6,7,2,5,5,8,1,9,7,6,

%U 2,7,4,0,5,8,3,3,4,8,6,4,6,1,0,4,1

%N Decimal expansion of a coefficient associated with the asymptotics of the variance of the distance between a vertex and the root of a random rooted tree.

%D Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, p. 304.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Tree.html">Tree</a>.

%F Variance of distance for n vertices ~ ((4-Pi)/(4*Pi))*(2*Pi/beta)^(2/3)*n.

%e 0.35296222290587711160803487440499612929275253953062322338956725581976274...

%t beta = 0.53494960614230701455037971105206839814311651405699009397707681023752321788064067239783; (* after A086308 and _Vaclav Kotesovec_'s computation *) RealDigits[((4-Pi)/(4*Pi))*(2*Pi/beta)^(2/3), 10, 85] // First

%Y Cf. A086308, A245652.

%K nonn,cons,more

%O 0,1

%A _Jean-François Alcover_, Jul 28 2014