A261340 Decimal expansion of the radius of convergence of the generating function of A000598, the number of rooted ternary trees of n vertices.

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

Offset: 0

Author

Jean-François Alcover, Aug 15 2015

Keywords

• nonn
• cons

Examples

			0.35518174231437739288224447364763263670874695417532...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.6 Otter's tree enumeration constants, p. 298.

Links

• Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, 2009; p. 478.

Crossrefs

Cf. A000598, A000642, A002094, A121331, A244399.

Programs

Mathematica

digits = 97; m = 2 digits + 10; For[gf = 0; i = 0, i <= m, i++, gf = Series[1 + x*(gf^3/6 + (gf /. x -> x^2)*gf/2 + (gf /. x -> x^3)/3), {x, 0, m + 1}] // Normal];
g[r_] := Module[{r2, r3, X, ym}, r2 = gf /. x -> r^2; r3 = gf /. x -> r^3; X[y_] = (y - 1)/(y^3/6 + r2*y/2 + r3/3); ym = y /. FindRoot[X'[y] == 0, {y, 2}, WorkingPrecision -> digits + 5]; X[ym]]; rho = FixedPoint[g, 1/3, SameTest -> (Abs[#1 - #2] < 10^-digits &)]; RealDigits[rho, 10, digits] // First

Extensions

More digits from Vaclav Kotesovec, Aug 15 2015

More digits and Mma code updated by Jean-François Alcover, Apr 18 2016