0,2

Contribution from M. F. Hasler (MHasler(AT)univ-ag.fr), 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)

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

Winston C. Yang (paper in preparation).

N. J. A. Sloane, Classic Sequences

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 (MHasler(AT)univ-ag.fr), May 02 2009]

(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]

(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]

Sequence in context: A114211 A034131 A161142 this_sequence A054498 A134139 A097125

Adjacent sequences: A018207 A018208 A018209 this_sequence A018211 A018212 A018213

nonn

N. J. A. Sloane (njas(AT)research.att.com), Winston C. Yang (yang(AT)math.wisc.edu)