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A202844 Number of secondary structures of size n having no stacks of length 3. 6
1, 1, 1, 2, 4, 8, 17, 36, 79, 179, 407, 935, 2173, 5089, 12005, 28500, 68022, 163154, 393060, 950652, 2307454, 5618906, 13723145, 33607242, 82507764, 203028034, 500659653, 1237053269, 3062204227, 7593229687, 18858944533, 46909741893, 116848688876, 291449697298 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

For "secondary structure" and "stack" see the Hofacker et al. reference, p. 209.

LINKS

Table of n, a(n) for n=0..33.

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

Cf. A202838, A202839, A202840, A202841, A202842, A202843

Sequence in context: A002845 A072925 A002955 * A093951 A137255 A247298

Adjacent sequences:  A202841 A202842 A202843 * A202845 A202846 A202847

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 25 2011

STATUS

approved

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Last modified December 2 01:48 EST 2020. Contains 338864 sequences. (Running on oeis4.)