A291836 - OEIS

%I #16 Sep 05 2017 03:31:26

%S 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,

%T 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,

%U 6,2,6,2,1,5,8,3,1,0,7,0

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

%H Gheorghe Coserea, <a href="/A291836/b291836.txt">Table of n, a(n) for n = 2..55001</a>

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

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

%e 26.18411255565814849687701423391145...

%o (PARI)

%o x(t)     = (1+3*t)*(1/t-1)^3/16;

%o y(t)     = {

%o   my(y1  = t^2 * (1-t) * (18 + 36*t + 5*t^2),

%o      y2  = 2 * (3+t) * (1+2*t) * (1+3*t)^2);

%o   (1+2*t)/((1+3*t) * (1-t)) * exp(-y1/y2) - 1;

%o };

%o N=80; default(realprecision, N+100); t0=solve(t=.62, .63, y(t)-1);

%o r=1/x(t0); eval(select(x->(x != "."), Vec(Str(r))[1..-101]))

%Y Cf. A096331, A266389, A291835.

%K nonn,cons

%O 2,1

%A _Gheorghe Coserea_, Sep 03 2017