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A267410 Decimal expansion of the constant describing the variance of the number of edges of a random labeled planar graph on n vertices. 3
4, 3, 0, 3, 4, 7, 1, 6, 9, 7, 2, 9, 2, 0, 1, 0, 6, 6, 8, 4, 3, 0, 8, 9, 9, 8, 2, 1, 7, 3, 7, 8, 7, 4, 3, 3, 3, 9, 9, 4, 3, 0, 1, 3, 9, 2, 5, 5, 8, 5, 3, 4, 6, 2, 2, 4, 8, 8, 5, 4, 2, 2, 6, 5, 6, 1, 2, 5, 8, 9, 7, 6, 4, 4, 6, 4, 6, 3, 9, 3, 8, 6, 7, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..51001

Omer Gimenez, Marc Noy, Asymptotic enumeration and limit laws of planar graphs, J. Amer. Math. Soc. 22 (2009), 309-329.

FORMULA

Equals lim Var(Xn)/n, where Xn is the number of edges of a random labeled planar graph with n vertices.

Equals Kl(A266389), where function t->Kl(t) is defined in the PARI code.

EXAMPLE

0.4303471697292...

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));

Kl(t)  = (-R''(t) + R'(t)*Y''(t)/Y'(t))/(R(t)*Y'(t)^2) + Km(t) + Km(t)^2;

Kl(A266389)

CROSSREFS

Cf. A266389, A266390, A267409, A267412.

Sequence in context: A199443 A142723 A296228 * A016697 A086466 A330392

Adjacent sequences:  A267407 A267408 A267409 * A267411 A267412 A267413

KEYWORD

nonn,cons

AUTHOR

Gheorghe Coserea, Jan 13 2016

STATUS

approved

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Last modified July 7 14:34 EDT 2020. Contains 335495 sequences. (Running on oeis4.)