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A202840 Number of secondary structures of size n having no stacks of length 1. 6
1, 1, 1, 1, 1, 2, 4, 8, 14, 23, 38, 65, 117, 214, 391, 708, 1278, 2318, 4238, 7803, 14419, 26684, 49433, 91736, 170656, 318280, 594905, 1113868, 2088554, 3921505, 7373367, 13883045, 26174600, 49408932, 93372078, 176637791, 334491586, 634023965, 1202894908, 2284187117 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

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

a(n) = A202838(n,0).

LINKS

Table of n, a(n) for n=0..39.

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^4/(1-z^2).

EXAMPLE

a(5)=2; 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; they have 0,1,1,1,1,1,1,0 stacks of length 1, respectively.

MAPLE

f := 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, 42)): seq(coeff(Gser, z, n), n = 0 .. 39);

CROSSREFS

Cf. A202838, A202839, A202841, A202842, A202843, A202844

Sequence in context: A055291 A091773 A107055 * A018153 A101687 A096461

Adjacent sequences:  A202837 A202838 A202839 * A202841 A202842 A202843

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Dec 25 2011

STATUS

approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)