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Search: id:A005994
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| A005994 |
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Alkane (or paraffin) numbers l(7,n).
(Formerly M2774)
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+0
4
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| 1, 3, 9, 19, 38, 66, 110, 170, 255, 365, 511, 693, 924, 1204, 1548, 1956, 2445, 3015, 3685, 4455, 5346, 6358, 7514, 8814, 10283, 11921, 13755, 15785, 18040, 20520, 23256, 26248, 29529, 33099, 36993, 41211, 45790, 50730, 56070, 61810, 67991
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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S. J. Cyvin et al., Polygonal systems including the corannulene ... homologs ..., Z. Naturforsch., 52a (1997), 867-873.
S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
N. J. A. Sloane, Classic Sequences
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FORMULA
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G.f.: (1+x^2)/((1-x)^3*(1-x^2)^2).
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(-5-n)=a(n) . - Michael Somos Mar 08 2007
Euler transform of length 4 sequence [ 3, 3, 0, -1]. - Michael Somos Mar 08 2007
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MAPLE
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(Maple) a := n -> (Matrix([[1, 0$4, 1, 3]]).Matrix(7, (i, j)-> if (i=j-1) then 1 elif j=1 then [3, -1, -5, 5, 1, -3, 1][i] else 0 fi)^n)[1, 1]; seq (a(n), n=0..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 31 2008]
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PROGRAM
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(PARI) {a(n)=if(n<-4, n=-5-n); polcoeff( (1+x^2)/((1-x)^3*(1-x^2)^2)+x*O(x^n), n)} /* Michael Somos Mar 08 2007 */
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CROSSREFS
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Sequence in context: A062748 A014540 A115238 this_sequence A080010 A135117 A038163
Adjacent sequences: A005991 A005992 A005993 this_sequence A005995 A005996 A005997
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas, Winston C. Yang (yang(AT)math.wisc.edu)
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