OFFSET
0,8
COMMENTS
a(n)=Sum(k*A097777(n,k), k>=0).
FORMULA
G.f.=z^5*g^3*(g-1)/[(1-z)(1-z^2*g^2)], where g=1+zg+z^2*g(g-1).
EXAMPLE
a(6)=1 because among the 17 (=A004148(6)) peakless Motzkin paths of length 6 only UHUHDD contains subwords of type UH^jU for some j>0 (here D=(1,-1)).
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 05 2011
STATUS
approved