A058965 Continued fraction expansion of series-parallel constant.

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, 2

Offset: 0

Author

N. J. A. Sloane, E. M. Rains, Jan 14 2001

Keywords

• nonn
• cofr
• more

Examples

			Constant is 0.2808326669842003553932...
		

References

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

Links

• Steven R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author]
• O. Golinelli, Asymptotic behavior of two-terminal series-parallel networks, arXiv:cond-mat/9707023 [cond-mat.stat-mech], 1997.

Crossrefs

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

Formula

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