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 A098051 Number of peakless Motzkin paths with no U H...HU's where U=(1,1) and H=(1,0) (can be easily expressed using RNA secondary structure terminology). 1
 1, 1, 1, 2, 4, 8, 16, 32, 65, 134, 280, 592, 1264, 2722, 5906, 12900, 28344, 62608, 138949, 309692, 692905, 1555718, 3504016, 7915182, 17927154, 40702926, 92623758, 211217180, 482593474, 1104640484, 2532768508, 5816447840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS I. L. Hofacker, P. Schuster and P. F. Stadler, Combinatorics of RNA secondary structures, Discrete Appl. Math., 88, 1998, 207-237. P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discrete Math., 26 (1979), 261-272. M. Vauchassade de Chaumont and G. Viennot, Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire, Sem. Loth. Comb. B08l (1984) 79-86. [Formerly: Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, p. 79-86.] FORMULA G.f.: G=G(z) satisfies G=1+zG+z^2*G[G-1-zG+z/(1-z)]. EXAMPLE a(4)=4 because we have HHHH, UHDU, HUHD and UHHD; a(6)=16 because among all 17 peakless Motzkin paths of length 6 (see A004148) only (UHU)HDD does not qualify. MAPLE G:=(1-2*z+2*z^2-2*z^3-sqrt(1-4*z+4*z^2-4*z^5+4*z^6))/2/z^2/(1-z)^2: Gser:=series(G, z=0, 35): 1, seq(coeff(Gser, z^n), n=1..32); CROSSREFS Cf. A004148. Sequence in context: A195904 A101333 A023421 * A329053 A084637 A100137 Adjacent sequences:  A098048 A098049 A098050 * A098052 A098053 A098054 KEYWORD nonn AUTHOR Emeric Deutsch, Sep 11 2004 STATUS approved

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Last modified April 14 06:59 EDT 2021. Contains 342946 sequences. (Running on oeis4.)