A291836 Decimal expansion of exponential growth rate of the number of 2-connected planar graphs on n labeled nodes.

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

Offset

2,1

Links

Gheorghe Coserea, Table of n, a(n) for n = 2..55001

E. A. Bender, Z. Gao and N. C. Wormald, The number of labeled 2-connected planar graphs, Electron. J. Combin., 9 (2002), #R43.

Formula

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

Constant r where A096331(n) ~ A291835 * n^(-7/2) * r^n * n!.

Example

26.18411255565814849687701423391145...

Prog

(PARI)
x(t)     = (1+3*t)*(1/t-1)^3/16;
y(t)     = {
  my(y1  = t^2 * (1-t) * (18 + 36*t + 5*t^2),
     y2  = 2 * (3+t) * (1+2*t) * (1+3*t)^2);
  (1+2*t)/((1+3*t) * (1-t)) * exp(-y1/y2) - 1;
};
N=80; default(realprecision, N+100); t0=solve(t=.62, .63, y(t)-1);
r=1/x(t0); eval(select(x->(x != "."), Vec(Str(r))[1..-101]))

Crossrefs

Cf. A096331, A266389, A291835.

Sequence in context: A136765 A011041 A363996 * A100831 A136763 A109530

Adjacent sequences: A291833 A291834 A291835 * A291837 A291838 A291839

Keyword

nonn,cons

Author

Gheorghe Coserea, Sep 03 2017

Status

approved