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 A190161 Number of subwords of  type uh^ju and dh^jd (j>=1), where u=(1,1), h=(1,0), and d=(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, 2, 10, 34, 104, 300, 834, 2270, 6094, 16206, 42818, 112606, 295138, 771616, 2013550, 5246954, 13657882, 35522364, 92331014, 239875614, 622971814, 1617463986, 4198716114, 10897812738, 28282859174, 73398069768, 190474295608, 494298218888, 1282776917922 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS a(n)=Sum(k*A097100(n,k), k>=0). LINKS FORMULA G.f.: G(z)=2z^3*g^3*(g-1)/[(1-z)(1-z^2*g^2)], where g=1+zg+z^2*g(g-1). EXAMPLE a(6)=2 because among the 17 (=A004148(6)) peakless  Motzkin paths of length 6 only (uhu)hdd and uuh(dhd) have subwords of the prescribed type (shown between parentheses). MAPLE eq := g = 1+z*g+z^2*g*(g-1): g := RootOf(eq, g): gser := series(2*z^5*g^3*(g-1)/((1-z)*(1-z^2*g^2)), z = 0, 38): seq(coeff(gser, z, n), n = 0 .. 33); CROSSREFS Cf. A097100, A004148 Sequence in context: A211905 A022498 A036799 * A196969 A119193 A124634 Adjacent sequences:  A190158 A190159 A190160 * A190162 A190163 A190164 KEYWORD nonn AUTHOR Emeric Deutsch, May 05 2011 STATUS approved

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Last modified June 22 07:09 EDT 2021. Contains 345374 sequences. (Running on oeis4.)