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 A190162 Number of peakless Motzkin paths of length n containing no subwords of type dh^ju (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, 17, 36, 77, 167, 365, 805, 1790, 4008, 9033, 20477, 46663, 106843, 245691, 567194, 1314086, 3054442, 7120951, 16647056, 39015476, 91654385, 215780420, 509033640, 1203085539, 2848445175, 6755095119, 16044373511, 38162885226, 90897048648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n)=A098083(n,0). LINKS Table of n, a(n) for n=0..33. FORMULA G.f.: G=G(z) satisfies the equation G=1+zG+z^2*(G-1)[(1-z)G+z/(1-z)]. D-finite with recurrence (n+2)*a(n) +5*(-n-1)*a(n-1) +2*(4*n+1)*a(n-2) +(-6*n+5)*a(n-3) +(8*n-27)*a(n-4) +2*(-7*n+31)*a(n-5) +(13*n-71)*a(n-6) +(-7*n+47)*a(n-7) +(3*n-25)*a(n-8) +(-n+9)*a(n-9)=0. - R. J. Mathar, Jul 22 2022 EXAMPLE a(7)=36 because among the 37 (=A004148(7)) peakless Motzkin paths of length 7 only uh(dhu)hd has a subword of the forbidden type (shown between parentheses). MAPLE eq := G = 1+z*G+z^2*(G-1)*((1-z)*G+z/(1-z)): G := RootOf(eq, G): Gser := series(G, z=0, 38): seq(coeff(Gser, z, n), n = 0 .. 33); CROSSREFS Cf. A098083, A004148 Sequence in context: A226729 A063457 A262735 * A275691 A251691 A157904 Adjacent sequences: A190159 A190160 A190161 * A190163 A190164 A190165 KEYWORD nonn AUTHOR Emeric Deutsch, May 05 2011 STATUS approved

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Last modified September 30 19:11 EDT 2023. Contains 365793 sequences. (Running on oeis4.)