login
A291836
Decimal expansion of exponential growth rate of the number of 2-connected planar graphs on n labeled nodes.
5
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
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
KEYWORD
nonn,cons
AUTHOR
Gheorghe Coserea, Sep 03 2017
STATUS
approved