A291840 Decimal expansion of the constant c in the asymptotic formula for A291839.

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

Offset

1,1

Links

Gheorghe Coserea, Table of n, a(n) for n = 1..55000

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

Constant c where A291839(n) ~ c*n + o(sqrt(n)).

Example

2.262875832562621246302333358384...

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;
};
alpha(t) = 144 + 592*t + 664*t^2 + 135*t^3 + 6*t^4 - 5*t^5;
mu(t)    = {
  my(mu1 = (1+t) * (3+t)^2 * (1+2*t)^2 * (1+3*t)^2 / t^3, y0 = y(t));
  mu1 * y0 / ((1 + y0) * alpha(t));
};
N=79; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
c=mu(t0); eval(select(x->(x != "."), Vec(Str(c))[1..-101]))

Crossrefs

Cf. A100960, A266389, A291839.

Sequence in context: A071052 A305984 A193388 * A208448 A096869 A345315

Adjacent sequences: A291837 A291838 A291839 * A291841 A291842 A291843

Keyword

nonn,cons

Author

Gheorghe Coserea, Sep 05 2017

Status

approved