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).

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).

Links

Table of n, a(n) for n=0..33.

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

Cf. A097777, A004148

Sequence in context: A034335 A337033 A190173 * A290186 A178703 A248875

Adjacent sequences: A187254 A187255 A187256 * A187258 A187259 A187260

Keyword

nonn

Author

Emeric Deutsch, May 05 2011

Status

approved