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A018213
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Alkane (or paraffin) numbers l(12,n).
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3
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1, 5, 30, 110, 365, 1001, 2520, 5720, 12190, 24310, 46252, 83980, 147070, 248710, 408760, 653752, 1021735, 1562275, 2343770, 3453450, 5008003, 7153575, 10080720, 14024400, 19284460, 26225628, 35304920, 47071640
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Equals (1/2) * ((A000582) + (A000332 interleaved with zeros)) = (1/2) * ((1, 10, 55, 220, 715...) + (1, 0, 5, 0, 15,...)); where A000582 = binomial(n,9) and A000332 = binomial(n,4).
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REFERENCES
| S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
Winston C. Yang (paper in preparation).
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LINKS
| N. J. A. Sloane, Classic Sequences
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FORMULA
| l(c, r) = 1/2 binomial(c+r-3, r) + 1/2 d(c, r), where d(c, r) is binomial((c + r - 3)/2, r/2) if c is odd and r is even, 0 if c is even and r is odd, binomial((c + r - 4)/2, r/2) if c is even and r is even, binomial((c + r - 4)/2, (r - 1)/2) if c is odd and r is odd.
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CROSSREFS
| Sequence in context: A174002 A030506 A062990 * A047661 A000649 A027173
Adjacent sequences: A018210 A018211 A018212 * A018214 A018215 A018216
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Winston C. Yang (yang(AT)math.wisc.edu)
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