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A098057 Number of peakless Motzkin paths with no U H^j U, no D H^j D and no D H^jU (j>0), where U=(1,1), D=(1,-1) and H=(1,0) (can be easily expressed using RNA secondary structure terminology). 2
1, 1, 1, 2, 4, 8, 15, 27, 48, 84, 147, 257, 451, 796, 1413, 2526, 4544, 8226, 14978, 27417, 50434, 93183, 172865, 321857, 601263, 1126644, 2116968, 3987960, 7530200, 14249649, 27019301, 51327965, 97676156, 186177568, 355406479, 679425009 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

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.

FORMULA

G.f.: [1-z+z^2-4z^3+2z^4-sqrt(1-2z-z^2+2z^3+z^4-4z^5+4z^6)]/[2z^2*(1-z)^3].

EXAMPLE

a(4)=4 because we have HHHH, UHDU, HUHD and UHHD; a(6)=15 because from all 17 peakless Motzkin paths of length 6 (see A004148) only (UHU)HDD and UUH(DHD) do not qualify.

CROSSREFS

Cf. A004148.

Sequence in context: A344611 A182716 A143281 * A289692 A074029 A248729

Adjacent sequences:  A098054 A098055 A098056 * A098058 A098059 A098060

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Sep 11 2004

STATUS

approved

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Last modified June 20 09:10 EDT 2021. Contains 345162 sequences. (Running on oeis4.)