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A202842 Number of secondary structures of size n having no stacks of length 2. 6
1, 1, 1, 2, 4, 7, 14, 31, 66, 142, 316, 708, 1593, 3625, 8314, 19165, 44433, 103557, 242376, 569514, 1343099, 3177766, 7540845, 17943506, 42804078, 102345017, 245233366, 588785677, 1416247791, 3412495415, 8235829927, 19906780104, 48185131721, 116790380824, 283432579807 (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.

a(n) = A202841(n,0).

LINKS

Table of n, a(n) for n=0..34.

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^2+z^4)/(1-z^2).

EXAMPLE

a(5)=7; 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; only the last one has a stack of length 2.

MAPLE

f := z^2*(1-z^2+z^4)/(1-z^2): eq := G = 1+z*G+f*G*(G-1)/(1+f): G := RootOf(eq, G): Gser := simplify(series(G, z = 0, 38)): seq(coeff(Gser, z, n), n = 0 .. 34);

CROSSREFS

Cf. A202838, A202839, A202840, A202841, A202843, A202844

Sequence in context: A247295 A120262 A202849 * A013326 A202973 A074663

Adjacent sequences:  A202839 A202840 A202841 * A202843 A202844 A202845

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 25 2011

STATUS

approved

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Last modified June 5 09:13 EDT 2020. Contains 334829 sequences. (Running on oeis4.)