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

Author

Jean-François Alcover, Jul 28 2014

Keywords

• nonn
• cons
• more

Examples

			0.35296222290587711160803487440499612929275253953062322338956725581976274...
		

References

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

Links

• Eric Weisstein's World of Mathematics, Tree.

Crossrefs

Cf. A086308, A245652.

Programs

Mathematica

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

Formula

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