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URL: https://oeis.org/A267409

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A267409
Decimal expansion of the constant describing the average number of edges of a random labeled planar graph with n vertices.
3
2, 2, 1, 3, 2, 6, 5, 2, 3, 8, 5, 7, 4, 4, 2, 1, 7, 8, 7, 6, 1, 6, 7, 4, 9, 0, 4, 7, 6, 3, 1, 9, 5, 2, 6, 6, 3, 8, 6, 5, 1, 9, 5, 6, 2, 5, 1, 1, 5, 5, 4, 2, 1, 5, 9, 2, 7, 9, 7, 1, 8, 2, 7, 1, 7, 7, 1, 9, 5, 9, 7, 6, 4, 8, 7, 0, 3, 8, 8, 5, 0, 8, 3, 2
OFFSET
1,1
LINKS
Omer Gimenez, Marc Noy, Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc. 22 (2009), 309-329.
FORMULA
Equals lim E[Xn]/n, where Xn is the number of edges of a random labeled planar graph with n vertices.
Equals Km(A266389), where function t->Km(t) is defined in the PARI code.
EXAMPLE
2.21326523857442...
PROG
(PARI)
A266389= 0.6263716633;
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;
A1(t) = log(1+t) * (3*t-1) * (1+t)^3 / (16*t^3);
A2(t) = log(1+2*t) * (1+3*t) * (1-t)^3 / (32*t^3);
A3(t) = (1-t) * (185*t^4 + 698*t^3 - 217*t^2 - 160*t + 6);
A4(t) = 64*t * (1+3*t)^2 * (3+t);
A(t) = A1(t) + A2(t) + A3(t) / A4(t);
R(t) = 1/16 * sqrt(1+3*t) * (1/t - 1)^3 * exp(A(t));
Km(t) = -R'(t)/(R(t)*Y'(t));
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Gheorghe Coserea, Jan 13 2016
STATUS
approved