OFFSET
0,4
COMMENTS
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(t, z) satisfies G = 1 + z*G + z^2*(G-1)*(G - (1-t)*z*(G-z*G-1)/(1-z)).
EXAMPLE
Triangle starts:
1;
1;
1;
2;
4;
8;
17;
36, 1;
77, 5;
167, 18
T(8,1)=5 because we have UH(DHU)HHD, HUH(DHU)HD, UH(DHHU)HD, UH(DHU)HDH and UHH(DHU)HD (the required subwords are shown between parentheses).
MAPLE
eq := G = 1+z*G+z^2*(G-1)*(G-(1-t)*z*(G-1-z*G)/(1-z)): G := RootOf(eq, G): Gser := simplify(series(G, z = 0, 23)): for n from 0 to 20 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 20 do seq(coeff(P[n], t, j), j = 0 .. degree(P[n])) end do; # yields sequence in triangular form
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Sep 13 2004
STATUS
approved