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
Examples
1.1365599187866006432360343661409534473438228750343833261672638156843...
References
- Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's Tree Enumeration Constants, pp. 304, 308.
Links
- Eric Weisstein's World of Mathematics, Tree.
Programs
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Mathematica
beta = 0.53494960614230701455037971105206839814311651405699009397707681023752321788064067239783; (* after A086308 and Vaclav Kotesovec's computation *) RealDigits[(1/2)*(2*Pi/beta)^(1/3), 10, 85] // First
Formula
Average distance for n vertices ~ (1/2)*(2*Pi/beta)^(1/3)*n^(1/2).