OFFSET
0,5
FORMULA
G.f.=2(1-z)/[1-2z+3z^2+(1-z)sqrt(1-2z-3z^2)].
D-finite with recurrence 2*(n+2)*a(n) +2*(-5*n-4)*a(n-1) +(13*n+2)*a(n-2) +(n-16)*a(n-3) +3*(-5*n+14)*a(n-4) +9*(n-4)*a(n-5)=0. - R. J. Mathar, Jul 24 2022
EXAMPLE
a(5)=6 because among the 21 Motzkin paths of length 5 only the following have
no U(H^p)D for any p>=0: HHHHH, HUUDD, UUDDH, UHUDD, UUDHD and UUHDD.
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 27 2003
STATUS
approved