A346916 Decimal expansion of the limit as N->oo of the mean number of singletons per forest in the rooted forests of N vertices.

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

Offset: 0

Author

Kevin Ryde, Aug 07 2021

Keywords

• nonn
• cons

Comments

There are A000081(N+1) rooted forests of N vertices and A087803(N) singletons in those forests, so the present constant is S = lim_{N->oo} A087803(N) / A000081(N+1).

The respective asymptotic formulas for A000081 and A087803 show that S = 1/(d-1) where d=A051491 is the growth power of rooted trees and forests.

Examples

			0.5113087993412405989719999189667575...
		

Links

• Kevin Ryde, Table of n, a(n) for n = 0..1797

Crossrefs

Cf. A051491 (rooted tree growth), A346915 (vpar mems).

Cf. A000081 (number of rooted forests), A087803 (total singletons).

Cf. A261124 (mean number of component trees).

Formula

Equals 1/(A051491 - 1).

Equals (A346915 - 2)/3.