%I A018210
%S A018210 1,4,16,44,110,236,472,868,1519,2520,4032,6216,9324,13608,19440,
%T A018210 27192,37389,50556,67408,88660,115258,148148,188552,237692,297115,
%U A018210 368368,453376,554064,672792,811920,974304,1162800,1380825,1631796
%N A018210 Alkane (or paraffin) numbers l(9,n).
%C A018210 Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), May 02 2009: 
               (Start)
%C A018210 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.
%C A018210 Third differences are A002412([n/2]). (End)
%D A018210 S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, 
               Chem. Ber. 30 (1897), 1917-1926.
%D A018210 Winston C. Yang (paper in preparation).
%H A018210 N. J. A. Sloane, <a href="classic.html#LOSS">Classic Sequences</a>
%F A018210 G.f.: (1+3*x^2)/(1-x)^4/(1-x^2)^3 [ N. J. A. Sloane (njas(AT)research.att.com) 
               ]
%F A018210 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 A018210 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 (MHasler(AT)univ-ag.fr), May 02 2009]
%p A018210 (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]
%o A018210 (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 (MHasler(AT)univ-ag.fr), May 02 2009]
%Y A018210 Sequence in context: A114211 A034131 A161142 this_sequence A054498 A134139 
               A097125
%Y A018210 Adjacent sequences: A018207 A018208 A018209 this_sequence A018211 A018212 
               A018213
%K A018210 nonn
%O A018210 0,2
%A A018210 N. J. A. Sloane (njas(AT)research.att.com), Winston C. Yang (yang(AT)math.wisc.edu)