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Search: id:A018211
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| A018211 |
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Alkane (or paraffin) numbers l(10,n). |
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+0
3
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| 1, 4, 20, 60, 170, 396, 868, 1716, 3235, 5720, 9752, 15912, 25236, 38760, 58200, 85272, 122661, 173052, 240460, 328900, 444158, 592020, 780572, 1017900, 1315015, 1682928, 2136304, 2689808, 3362600, 4173840, 5148144, 6310128
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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
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N. J. A. Sloane, Classic Sequences
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FORMULA
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G.f.: (1+6*x^2+x^4)/((1-x)^4*(1-x^2)^4) [ N. J. A. Sloane (njas(AT)research.att.com) ]
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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MAPLE
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(Maple) a := n -> (Matrix([[1, 0$7, -1, -4, -20, -60]]).Matrix(12, (i, j)-> if (i=j-1) then 1 elif j=1 then [4, -2, -12, 17, 8, -28, 8, 17, -12, -2, 4, -1][i] else 0 fi)^n)[1, 1]; seq (a(n), n=0..31); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
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CROSSREFS
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Sequence in context: A060122 A066970 A033488 this_sequence A135507 A131479 A055538
Adjacent sequences: A018208 A018209 A018210 this_sequence A018212 A018213 A018214
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Winston C. Yang (yang(AT)math.wisc.edu)
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