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A266389 Solution of the equation y(t) = 1, where function y(t) is defined in the Comments section. 12

%I #32 Sep 03 2017 21:45:11

%S 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 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 2,1,5,3,0,0,2,4,2,7,7,6,7,9,0

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

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

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

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

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

%H Gheorghe Coserea, <a href="/A266389/b266389.txt">Table of n, a(n) for n = 0..54301</a>

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

%e 0.62637166330...

%o (PARI)

%o y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2);

%o y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2;

%o y(t) = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1;

%o N=83; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);

%o eval(Vec(Str(t0))[3..-101]) \\ _Gheorghe Coserea_, Sep 03 2017

%Y Cf. A266390, A266391, A266392.

%K nonn,cons

%O 0,1

%A _Gheorghe Coserea_, Dec 28 2015

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