OFFSET
0,3
COMMENTS
a(n)=A182903(n,0).
REFERENCES
M. Bona and A. Knopfmacher, On the probability that certain compositions have the same number of parts, Ann. Comb., 14 (2010), 291-306.
E. Munarini, N. Zagaglia Salvi, On the rank polynomial of the lattice of order ideals of fences and crowns, Discrete Mathematics 259 (2002), 163-177.
FORMULA
G.f.: g=1/sqrt(1-2z-z^2-z^4-2z^5+z^6).
Conjecture: n*a(n) +(n-2)*a(n-1) +(-7*n+10)*a(n-2) +3*(-n+2)*a(n-3) +(-n+2)*a(n-4) +(-5*n+14)*a(n-5) +(-5*n+18)*a(n-6) +3*(n-4)*a(n-7)=0. - R. J. Mathar, Jun 14 2016
EXAMPLE
a(3)=4. Indeed, denoting by h (H) the (1,0)-step of weight 1 (2), and U=(1,1), D=(1,-1), we have hhh, hH, Hh, and DU.
MAPLE
g := 1/sqrt(1-2*z-z^2-z^4-2*z^5+z^6): gser := series(g, z = 0, 35):seq(coeff(gser, z, n), n = 0 .. 30);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 16 2010
STATUS
approved