Search: id:A098057 Results 1-1 of 1 results found. %I A098057 %S A098057 1,1,1,2,4,8,15,27,48,84,147,257,451,796,1413,2526,4544,8226,14978, %T A098057 27417,50434,93183,172865,321857,601263,1126644,2116968,3987960,7530200, %U A098057 14249649,27019301,51327965,97676156,186177568,355406479,679425009 %N 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). %D A098057 I. L. Hofacker, P. Schuster and P. F. Stadler, Combinatorics of RNA secondary structures, Discrete Appl. Math., 88, 1998, 207-237. %D A098057 P. R. Stein and M. S. Waterman, On some new sequences generalizing the Catalan and Motzkin numbers, Discrete Math., 26, 1979, 261-272. %D A098057 M. Vauchassade de Chaumont and G. Viennot, Polynomes orthogonaux et problemes d'enumeration en biologie moleculaire, Publ. I.R.M.A. Strasbourg, 1984, 229/S-08, Actes 8e Sem. Lotharingien, pp. 79-86. %H A098057 M. Vauchassade de Chaumont and G. Viennot, Polynomes orthogonaux at problemes d'enumeration en biologie moleculaire, Sem. Loth. Comb. B08l (1984) 79-86. %F A098057 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]. %e A098057 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. %Y A098057 Cf. A004148. %Y A098057 Sequence in context: A001523 A000126 A143281 this_sequence A074029 A138653 A054159 %Y A098057 Adjacent sequences: A098054 A098055 A098056 this_sequence A098058 A098059 A098060 %K A098057 nonn %O A098057 0,4 %A A098057 Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 11 2004 Search completed in 0.001 seconds