A245653 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.

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

Offset

0,1

References

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

Links

Table of n, a(n) for n=0..84.

Eric Weisstein's World of Mathematics, Tree.

Formula

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

Example

0.35296222290587711160803487440499612929275253953062322338956725581976274...

Mathematica

beta = 0.53494960614230701455037971105206839814311651405699009397707681023752321788064067239783; (* after A086308 and Vaclav Kotesovec's computation *) RealDigits[((4-Pi)/(4*Pi))*(2*Pi/beta)^(2/3), 10, 85] // First

Crossrefs

Cf. A086308, A245652.

Sequence in context: A275846 A273668 A356472 * A209748 A065172 A026212

Adjacent sequences: A245650 A245651 A245652 * A245654 A245655 A245656

Keyword

nonn,cons,more

Author

Jean-François Alcover, Jul 28 2014

Status

approved