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A018210
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Alkane (or paraffin) numbers l(9,n).
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4
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1, 4, 16, 44, 110, 236, 472, 868, 1519, 2520, 4032, 6216, 9324, 13608, 19440, 27192, 37389, 50556, 67408, 88660, 115258, 148148, 188552, 237692, 297115, 368368, 453376, 554064, 672792, 811920, 974304, 1162800, 1380825, 1631796
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Contribution from M. F. Hasler (www.univ-ag.fr/~mhasler), May 02 2009: (Start)
Also, 6-th column of A159916, i.e. number of 6-element subsets of {1,...,n+6} whose elements add up to an odd integer.
Third differences are A002412([n/2]). (End)
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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
| G.f.: (1+3*x^2)/(1-x)^4/(1-x^2)^3 [ N. J. A. Sloane (njas(AT)research.att.com) ]
l(c, r) = 1/2 C(c+r-3, r) + 1/2 d(c, r), where d(c, r) is C((c + r - 3)/2, r/2) if c is odd and r is even, 0 if c is even and r is odd, C((c + r - 4)/2, r/2) if c is even and r is even, C((c + r - 4)/2, (r - 1)/2) if c is odd and r is odd.
a(2n)=(n+1)(n+2)(n+3)^2(4n^2+6n+5)/90, a(2n-1)=n(n+1)(n+2)(n+3)(4n^2+6n+5)/90. [From M. F. Hasler (www.univ-ag.fr/~mhasler), May 02 2009]
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MAPLE
| (Maple) a := n -> (Matrix([[1, 0$7, 3, 12]]).Matrix(10, (i, j)-> if (i=j-1) then 1 elif j=1 then [4, -3, -8, 14, 0, -14, 8, 3, -4, 1][i] else 0 fi)^n)[1, 1]; seq (a(n), n=0..33); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
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PROG
| (PARI) A018210(n)=(n+2)*(n+4)*(n+6)^2*(n^2+3*n+5)/1440-if(n%2, (n^2+7*n+11)/32) [From M. F. Hasler (www.univ-ag.fr/~mhasler), May 02 2009]
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CROSSREFS
| Sequence in context: A034131 A183536 A161142 * A054498 A134139 A097125
Adjacent sequences: A018207 A018208 A018209 * A018211 A018212 A018213
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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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