Search: id:A005994
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%I A005994 M2774
%S A005994 1,3,9,19,38,66,110,170,255,365,511,693,924,1204,1548,1956,2445,3015,
%T A005994 3685,4455,5346,6358,7514,8814,10283,11921,13755,15785,18040,20520,
%U A005994 23256,26248,29529,33099,36993,41211,45790,50730,56070,61810,67991
%N A005994 Alkane (or paraffin) numbers l(7,n).
%C A005994 Equals (1, 3, 6, 10, 15,...) convolved with (1, 0, 3, 0, 5,...). [From 
               Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 16 2009]
%D A005994 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005994 S. J. Cyvin et al., Polygonal systems including the corannulene ... homologs 
               ..., Z. Naturforsch., 52a (1997), 867-873.
%D A005994 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, 
               Chem. Ber. 30 (1897), 1917-1926.
%H A005994 T. D. Noe, <a href="b005994.txt">Table of n, a(n) for n=0..1000</a>
%H A005994 N. J. A. Sloane, <a href="classic.html#LOSS">Classic Sequences</a>
%F A005994 G.f.: (1+x^2)/((1-x)^3*(1-x^2)^2).
%F A005994 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.
%F A005994 a(-5-n)=a(n) . - Michael Somos Mar 08 2007
%F A005994 Euler transform of length 4 sequence [ 3, 3, 0, -1]. - Michael Somos 
               Mar 08 2007
%p A005994 (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]
%o A005994 (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 */
%Y A005994 Sequence in context: A146050 A147500 A115238 this_sequence A080010 A135117 
               A038163
%Y A005994 Adjacent sequences: A005991 A005992 A005993 this_sequence A005995 A005996 
               A005997
%K A005994 nonn,easy,nice
%O A005994 0,2
%A A005994 N. J. A. Sloane (njas(AT)research.att.com), Winston C. Yang (yang(AT)math.wisc.edu)

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