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A187257
Number of UH^jU's for some j>0, where U=(1,1) and H=(1,1), in all peakless Motzkin paths of length n (can be easily expressed using RNA secondary structure terminology).
1
0, 0, 0, 0, 0, 0, 1, 5, 17, 52, 150, 417, 1135, 3047, 8103, 21409, 56303, 147569, 385808, 1006775, 2623477, 6828941, 17761182, 46165507, 119937807, 311485907, 808731993, 2099358057, 5448906369, 14141429587, 36699034884, 95237147804, 247149109444, 641388458961
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