OFFSET
0,4
COMMENTS
a(n)=A098083(n,0).
FORMULA
G.f.: G=G(z) satisfies the equation G=1+zG+z^2*(G-1)[(1-z)G+z/(1-z)].
D-finite with recurrence (n+2)*a(n) +5*(-n-1)*a(n-1) +2*(4*n+1)*a(n-2) +(-6*n+5)*a(n-3) +(8*n-27)*a(n-4) +2*(-7*n+31)*a(n-5) +(13*n-71)*a(n-6) +(-7*n+47)*a(n-7) +(3*n-25)*a(n-8) +(-n+9)*a(n-9)=0. - R. J. Mathar, Jul 22 2022
EXAMPLE
a(7)=36 because among the 37 (=A004148(7)) peakless Motzkin paths of length 7 only uh(dhu)hd has a subword of the forbidden type (shown between parentheses).
MAPLE
eq := G = 1+z*G+z^2*(G-1)*((1-z)*G+z/(1-z)): G := RootOf(eq, G): Gser := series(G, z=0, 38): seq(coeff(Gser, z, n), n = 0 .. 33);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 05 2011
STATUS
approved