cp's OEIS Frontend

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

%I A291840 #11 Sep 06 2017 04:07:32
%S A291840 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,
%T A291840 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,
%U A291840 7,3,8,9,7,1,2,9,9,4,8
%N A291840 Decimal expansion of the constant c in the asymptotic formula for A291839.
%H A291840 Gheorghe Coserea, <a href="/A291840/b291840.txt">Table of n, a(n) for n = 1..55000</a>
%H A291840 E. A. Bender, Z. Gao and N. C. Wormald, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v9i1r43">The number of labeled 2-connected planar graphs</a>, Electron. J. Combin., 9 (2002), #R43.
%F A291840 Equals mu(A266389), where function t->mu(t) is defined in the PARI code.
%F A291840 Constant c where A291839(n) ~ c*n + o(sqrt(n)).
%e A291840 2.262875832562621246302333358384...
%o A291840 (PARI)
%o A291840 x(t)     = (1+3*t)*(1/t-1)^3/16;
%o A291840 y(t)     = {
%o A291840   my(y1  = t^2 * (1-t) * (18 + 36*t + 5*t^2),
%o A291840      y2  = 2 * (3+t) * (1+2*t) * (1+3*t)^2);
%o A291840   (1+2*t)/((1+3*t) * (1-t)) * exp(-y1/y2) - 1;
%o A291840 };
%o A291840 alpha(t) = 144 + 592*t + 664*t^2 + 135*t^3 + 6*t^4 - 5*t^5;
%o A291840 mu(t)    = {
%o A291840   my(mu1 = (1+t) * (3+t)^2 * (1+2*t)^2 * (1+3*t)^2 / t^3, y0 = y(t));
%o A291840   mu1 * y0 / ((1 + y0) * alpha(t));
%o A291840 };
%o A291840 N=79; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
%o A291840 c=mu(t0); eval(select(x->(x != "."), Vec(Str(c))[1..-101]))
%Y A291840 Cf. A100960, A266389, A291839.
%K A291840 nonn,cons
%O A291840 1,1
%A A291840 _Gheorghe Coserea_, Sep 05 2017