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

0,1

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.

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.

Formula

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

Example

0.62637166330...

Prog

(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

Crossrefs

Cf. A266390, A266391, A266392.

Sequence in context: A318385 A319262 A126664 * A198986 A236190 A198227

Adjacent sequences: A266386 A266387 A266388 * A266390 A266391 A266392

Keyword

nonn,cons

Author

Gheorghe Coserea, Dec 28 2015

Status

approved