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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 25 04:52 EDT 2021. Contains 345452 sequences. (Running on oeis4.)