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A001572
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Related to series-parallel networks.
(Formerly M2500 N0989)
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2
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1, 1, 1, 1, 3, 5, 17, 41, 127, 365, 1119, 3413, 10685, 33561, 106827, 342129, 1104347, 3584649, 11701369, 38374065, 126395259, 417908329, 1386618307, 4615388353, 15407188529, 51569669429, 173033992311, 581905285089, 1961034571967
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008: (Start)
Starting (1, 1, 1, 3, 5, 17,...) = the INVERTi transform of A000084: (1, 2, 4, 10, 24, 66,...).
Equals left border of triangle A144962 (End)
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| G.f.: 1 - Sum_{k=1..inf} a(k)*x^k = Product_{n=1..inf} (1-x^n)^A000669(n).
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CROSSREFS
| A000084, A144962 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 27 2008]
Sequence in context: A148522 A141160 A113275 * A131342 A005142 A165452
Adjacent sequences: A001569 A001570 A001571 * A001573 A001574 A001575
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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