%I A018211
%S A018211 1,4,20,60,170,396,868,1716,3235,5720,9752,15912,25236,38760,58200,
%T A018211 85272,122661,173052,240460,328900,444158,592020,780572,1017900,
%U A018211 1315015,1682928,2136304,2689808,3362600,4173840,5148144,6310128
%N A018211 Alkane (or paraffin) numbers l(10,n).
%D A018211 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, 
               Chem. Ber. 30 (1897), 1917-1926.
%D A018211 Winston C. Yang (paper in preparation).
%H A018211 N. J. A. Sloane, <a href="classic.html#LOSS">Classic Sequences</a>
%F A018211 G.f.: (1+6*x^2+x^4)/((1-x)^4*(1-x^2)^4) [ N. J. A. Sloane (njas(AT)research.att.com) 
               ]
%F A018211 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.
%p A018211 (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]
%Y A018211 Sequence in context: A060122 A066970 A033488 this_sequence A135507 A131479 
               A055538
%Y A018211 Adjacent sequences: A018208 A018209 A018210 this_sequence A018212 A018213 
               A018214
%K A018211 nonn
%O A018211 0,2
%A A018211 N. J. A. Sloane (njas(AT)research.att.com), Winston C. Yang (yang(AT)math.wisc.edu)