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 A190160 Number of peakless Motzkin paths of length n containing no subwords of  type uh^ju or dh^jd (j>=1), where u=(1,1), h=(1,0), and d=(1,-1) (can be easily expressed using RNA secondary structure terminology). 1
 1, 1, 1, 2, 4, 8, 15, 28, 53, 102, 199, 391, 773, 1537, 3075, 6189, 12525, 25473, 52037, 106737, 219761, 454041, 941089, 1956357, 4078010, 8522016, 17850512, 37471531, 78818748, 166102378, 350660371, 741503529, 1570402564, 3330730115, 7073941610, 15043298781 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n)=A097100(n,0). F% G.f.: G=G(z) satisfies the equation G=1+zG+z^2*G[z+(1-z)^2*(G-zG-1)]/(1-z). LINKS EXAMPLE a(6)=15 because among the 17 (=A004148(6)) peakless  Motzkin paths of length 6 only (uhu)hdd and uuh(dhd) have subwords of the forbidden type (shown between parentheses). MAPLE eq := G = 1+z*G+z^2*G*(z+(1-z)^2*(G-z*G-1))/(1-z): G := RootOf(eq, G): Gser := series(G, z = 0, 38): seq(coeff(Gser, z, n), n = 0 .. 35); CROSSREFS Cf. A097100, A004148 Sequence in context: A268393 A118870 A171857 * A332052 A088532 A271364 Adjacent sequences:  A190157 A190158 A190159 * A190161 A190162 A190163 KEYWORD nonn AUTHOR Emeric Deutsch, May 05 2011 STATUS approved

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Last modified June 25 10:09 EDT 2021. Contains 345453 sequences. (Running on oeis4.)