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!)
A267412 Decimal expansion of the constant describing the expected number of components in a random labeled planar graph on n vertices. 3
1, 0, 3, 7, 4, 3, 9, 3, 6, 6, 0, 2, 7, 5, 0, 6, 6, 1, 4, 8, 7, 3, 9, 0, 2, 0, 6, 5, 5, 9, 8, 7, 3, 1, 5, 0, 1, 4, 0, 3, 2, 2, 5, 9, 6, 0, 2, 4, 6, 3, 2, 0, 1, 2, 8, 3, 9, 3, 5, 6, 3, 2, 2, 7, 8, 0, 0, 3, 0, 6, 7, 5, 8, 7, 6, 1, 3, 8, 7, 5, 1, 0, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 1..51002

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], where Xn is the number of components in a random labeled planar graph with n vertices.

Equals 1 + C0(A266389), where function t->C0(t) is defined in the PARI code.

EXAMPLE

1.0374393660275...

PROG

(PARI)

A266389= 0.6263716633;

Xi(t)  = (1+3*t) * (1-t)^3 / ((16*t^3));

B01(t) = (3*t-1)^2 * (1+t)^6 * log(1+t)/(512*t^6);

B02(t) = (3*t^4 - 16*t^3 + 6*t^2 - 1) * log(1 + 3*t) / (32*t^3);

B03(t) = (1+3*t)^2 * (1-t)^6 * log(1+2*t) / (1024*t^6);

B04(t) = (1/4)*log(3+t) - (1/2)*log(t) - (3/8)*log(16);

B05(t) = (217*t^6 + 920*t^5 + 972*t^4 + 1436*t^3 + 205*t^2 - 172*t + 6);

B06(t) = (1-t)^2 / (2048 * t^4 * (1+3*t) * (3+t));

B0(t)  = B01(t) - B02(t) - B03(t) + B04(t) - B05(t) * B06(t);

B21(t) = (1-t)^3 * (3*t-1) * (1+3*t) * (1+t)^3 * log(1+t) / (256*t^6);

B22(t) = (1-t)^3 * (1+3*t) * log(1+3*t) / (32*t^3);

B23(t) = (1+3*t)^2 * (1-t)^6 * log(1+2*t) / (512*t^6);

B24(t) = (1-t)^4 * (185*t^4 + 698*t^3 - 217*t^2 - 160*t + 6);

B25(t) = 1024 * t^4 * (1+3*t) * (3+t);

B2(t)  = B21(t) - B22(t) + B23(t) + B24(t) / B25(t);

C0(t)  = Xi(t) + B0(t) + B2(t);

1 + C0(A266389)

CROSSREFS

Cf. A266389, A266390, A267409, A267410.

Sequence in context: A163335 A266273 A256676 * A087941 A278389 A021271

Adjacent sequences:  A267409 A267410 A267411 * A267413 A267414 A267415

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 June 3 05:29 EDT 2020. Contains 334798 sequences. (Running on oeis4.)