login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A267411 Decimal expansion of the constant describing the mean number of 2-connected components in a random connected labeled planar graph on n vertices. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
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: A126321 A335777 A248726 * A021260 A215633 A134878

Adjacent sequences:  A267408 A267409 A267410 * A267412 A267413 A267414

KEYWORD

nonn,cons

AUTHOR

Gheorghe Coserea, Jan 14 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 11 07:06 EDT 2020. Contains 335609 sequences. (Running on oeis4.)