A245652 Decimal expansion of a coefficient associated with the asymptotics of the average distance between a vertex and the root of a random rooted tree.

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

Offset

1,3

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=1..85.

Eric Weisstein's World of Mathematics, Tree.

Formula

Average distance for n vertices ~ (1/2)*(2*Pi/beta)^(1/3)*n^(1/2).

Example

1.1365599187866006432360343661409534473438228750343833261672638156843...

Mathematica

beta = 0.53494960614230701455037971105206839814311651405699009397707681023752321788064067239783; (* after A086308 and Vaclav Kotesovec's computation *) RealDigits[(1/2)*(2*Pi/beta)^(1/3), 10, 85] // First

Crossrefs

Cf. A086308, A245653.

Sequence in context: A291050 A268981 A353909 * A106109 A275925 A282581

Adjacent sequences: A245649 A245650 A245651 * A245653 A245654 A245655

Keyword

nonn,cons,more

Author

Jean-François Alcover, Jul 28 2014

Status

approved