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

Author

Gheorghe Coserea, Sep 05 2017

Keywords

• nonn
• cons

Examples

			2.262875832562621246302333358384...
		

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.

Crossrefs

Cf. A100960, A266389, A291839.

Programs

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]))

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)).