This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A202844 #11 Jan 22 2022 16:51:01 %S A202844 1,1,1,2,4,8,17,36,79,179,407,935,2173,5089,12005,28500,68022,163154, %T A202844 393060,950652,2307454,5618906,13723145,33607242,82507764,203028034, %U A202844 500659653,1237053269,3062204227,7593229687,18858944533,46909741893,116848688876,291449697298 %N A202844 Number of secondary structures of size n having no stacks of length 3. %C A202844 For "secondary structure" and "stack" see the Hofacker et al. reference, p. 209. %H A202844 I. L. Hofacker, P. Schuster and P. F. Stadler, <a href="https://doi.org/10.1016/S0166-218X(98)00073-0">Combinatorics of RNA secondary structures</a>, Discrete Appl. Math., 88, 1998, 207-237. %H A202844 P. R. Stein and M. S. Waterman, <a href="https://doi.org/10.1016/0012-365X(79)90033-5">On some new sequences generalizing the Catalan and Motzkin numbers</a>, Discrete Math., 26 (1979), 261-272. %F A202844 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). %F A202844 a(n) = A202843(n,0). %e A202844 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. %p A202844 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); %Y A202844 Cf. A202838, A202839, A202840, A202841, A202842, A202843. %K A202844 nonn %O A202844 0,4 %A A202844 _Emeric Deutsch_, Dec 25 2011