OFFSET
0,4
COMMENTS
For "secondary structure" and "stack" see the Hofacker et al. reference, p. 209.
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.
FORMULA
G.f.: G=G(z) satisfies G = 1+zG +fG(G-1)/(1+f), where f = z^2*(1-z^4+z^6)/(1-z^2).
a(n) = A202843(n,0).
EXAMPLE
a(5)=8; representing unpaired vertices by v and arcs by AA, BB, etc., the 8 (= A004148(5)) secondary structures of size 5 are vvvvv, AvAvv, vvAvA, AvvAv, vAvvA, AvvvA, vAvAv, ABvBA; none of them has stacks of length 3.
MAPLE
f := z^2*(1-z^4+z^6)/(1-z^2): eq := G = 1+z*G+f*G*(G-1)/(1+f): G := RootOf(eq, G): Gser := simplify(series(G, z = 0, 37)): seq(coeff(Gser, z, n), n = 0 .. 33);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 25 2011
STATUS
approved