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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 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.)