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A098051
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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).
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1
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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
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..31.
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.]
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FORMULA
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G.f.: G=G(z) satisfies G=1+zG+z^2*G[G-1-zG+z/(1-z)].
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EXAMPLE
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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.
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MAPLE
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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);
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CROSSREFS
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Cf. A004148.
Sequence in context: A195904 A101333 A023421 * A329053 A084637 A100137
Adjacent sequences: A098048 A098049 A098050 * A098052 A098053 A098054
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Sep 11 2004
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STATUS
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approved
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