0,2

Equals (1, 3, 6, 10, 15,...) convolved with (1, 0, 3, 0, 5,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 16 2009]

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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.

T. D. Noe, Table of n, a(n) for n=0..1000

N. J. A. Sloane, Classic Sequences

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

(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]

(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 */

Sequence in context: A146050 A147500 A115238 this_sequence A080010 A135117 A038163

Adjacent sequences: A005991 A005992 A005993 this_sequence A005995 A005996 A005997

nonn,easy,nice

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