A266389 Solution of the equation y(t) = 1, where function y(t) is defined in the Comments section.

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

Offset: 0

Author

Gheorghe Coserea, Dec 28 2015

Keywords

• nonn
• cons

Comments

For t in open interval (0,1) we have:

y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2).

y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2.

y(t) = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1.

Examples

			0.62637166330...
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 0..54301
• Omer Gimenez, Marc Noy, Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc. 22 (2009), 309-329.

Crossrefs

Cf. A266390, A266391, A266392.

Programs

PARI

y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2);
y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2;
y(t)  = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1;
N=83; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
eval(Vec(Str(t0))[3..-101]) \\ Gheorghe Coserea, Sep 03 2017

Formula

y(A266389) = 1, where function t->y(t) is defined in the Comments section.