cp's OEIS Frontend

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

%I A266389 #32 Sep 03 2017 21:45:11
%S A266389 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,
%T A266389 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,
%U A266389 2,1,5,3,0,0,2,4,2,7,7,6,7,9,0
%N A266389 Solution of the equation y(t) = 1, where function y(t) is defined in the Comments section.
%C A266389 For t in open interval (0,1) we have:
%C A266389 y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2).
%C A266389 y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2.
%C A266389 y(t)  = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1.
%H A266389 Gheorghe Coserea, <a href="/A266389/b266389.txt">Table of n, a(n) for n = 0..54301</a>
%H A266389 Omer Gimenez, Marc Noy, <a href="http://dx.doi.org/10.1090/S0894-0347-08-00624-3">Asymptotic enumeration and limit laws of planar graphs</a>, J. Amer. Math. Soc. 22 (2009), 309-329.
%F A266389 y(A266389) = 1, where function t->y(t) is defined in the Comments section.
%e A266389 0.62637166330...
%o A266389 (PARI)
%o A266389 y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2);
%o A266389 y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2;
%o A266389 y(t)  = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1;
%o A266389 N=83; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
%o A266389 eval(Vec(Str(t0))[3..-101]) \\ _Gheorghe Coserea_, Sep 03 2017
%Y A266389 Cf. A266390, A266391, A266392.
%K A266389 nonn,cons
%O A266389 0,1
%A A266389 _Gheorghe Coserea_, Dec 28 2015