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Continued fraction expansion of series-parallel constant.
2

%I #26 Jun 03 2017 15:29:12

%S 0,3,1,1,3,1,1,1,1,3,1,3,12,1,8,8,1,7,6,1,5,2,1,1,4,1,3,2,36,1,10,6,1,

%T 2

%N Continued fraction expansion of series-parallel constant.

%D J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226.

%D J. Riordan and C. E. Shannon, The number of two-terminal series-parallel networks, J. Math. Phys., 21 (1942), 83-93. Reprinted in Claude Elwood Shannon: Collected Papers, edited by N. J. A. Sloane and A. D. Wyner, IEEE Press, NY, 1993, pp. 560-570.

%H S. R. Finch, <a href="/A000084/a000084_2.pdf">Series-parallel networks</a>, July 7, 2003. [Cached copy, with permission of the author]

%H O. Golinelli, <a href="http://arXiv.org/abs/cond-mat/9707023">Asymptotic behavior of two-terminal series-parallel networks</a>, arXiv:cond-mat/9707023 [cond-mat.stat-mech], 1997.

%F This number, c, is defined by Product_{n=1..inf} (1-c^n)^(-A000669[n]) = 2.

%e Constant is 0.2808326669842003553932...

%Y See A058964 for decimal expansion. Cf. A000084, A000669.

%K nonn,cofr,more

%O 0,2

%A _N. J. A. Sloane_, E. M. Rains, Jan 14 2001