OFFSET
0,3
FORMULA
G.f. = z/[(1-z+z^2)sqrt((1+z+z^2)(1-3z+z^2))].
Conjecture: (-n+1)*a(n) +(3*n-4)*a(n-1) +2*(-n+1)*a(n-2) +3*(n-2)*a(n-3) +2*(-n+3)*a(n-4) +(3*n-8)*a(n-5) +(-n+3)*a(n-6)=0. - R. J. Mathar, Apr 09 2019
a(n) ~ phi^(2*n+2) / (4 * 5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, May 29 2022
EXAMPLE
a(4)=6 because in h'h'h'h', h'uhd, uhdh', and uhhd, where u=(1,1), h=(1,0), d=(1,-1), we have 4+1+1+0 h-steps at even levels (marked).
MAPLE
G := z/((1-z+z^2)*sqrt((1+z+z^2)*(1-3*z+z^2))): Gser := series(G, z=0, 36): seq(coeff(Gser, z, n), n=0..33);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 06 2011
STATUS
approved