A267411 Decimal expansion of the constant describing the mean number of 2-connected components in a random connected labeled planar graph on n vertices.

3, 9, 0, 5, 1, 8, 0, 2, 8, 2, 4, 5, 9, 1, 1, 1, 4, 7, 5, 5, 8, 5, 0, 6, 2, 6, 2, 1, 7, 3, 0, 9, 5, 0, 6, 7, 0, 4, 6, 4, 1, 1, 3, 0, 7, 6, 5, 2, 6, 0, 2, 9, 3, 5, 2, 1, 9, 0, 0, 6, 1, 9, 4, 5, 7, 1, 5, 5, 1, 4, 1, 5, 3, 5, 6, 1, 3, 6, 3, 1, 4, 2, 3, 9

Offset

-1,1

Links

Gheorghe Coserea, Table of n, a(n) for n = -1..51000

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 2-connected components in a random connected labeled planar graph with n vertices; also equals lim Var(Xn)/n.

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

Example

0.039051802824591114...

Prog

(PARI)
A266389= 0.6263716633;
Xi(t)  = (1+3*t) * (1-t)^3 / ((16*t^3));
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));
Kz(t)  = log(Xi(t)/R(t));
Kz(A266389)

Crossrefs

Cf. A266389, A266392.

Sequence in context: A335777 A358945 A248726 * A370468 A021260 A215633

Adjacent sequences: A267408 A267409 A267410 * A267412 A267413 A267414

Keyword

nonn,cons

Author

Gheorghe Coserea, Jan 14 2016

Status

approved