OFFSET
0,4
COMMENTS
Row sums are the RNA secondary structure numbers (A004148).
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.
FORMULA
G.f.: G=G(t, z) satisfies aG^2 + bG + c = 0, where a=z^2*(1-2z+z^2-z^3+tz-tz^2+tz^3), b=-(1-2z+2z^2-2z^3+tz^3), c=1-z.
EXAMPLE
Triangle starts:
1;
1;
1;
2;
4;
7,1;
12,5;
21,16;
37,44,1;
Row n >=2 has floor((n+1)/3) terms.
T(6,1)=5 because we have U(UHD)DH, HU(UHD)D, U(UHD)HD, UH(UHD)D and U(UHHD)D (the pertinent subword is shown between parentheses).
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Emeric Deutsch, Sep 13 2004
STATUS
approved