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Catafusenes (see reference for precise definition).
2

%I #29 May 29 2022 04:32:23

%S 0,0,0,1,12,94,612,3605,19992,106644,554184,2827902,14244120,71073860,

%T 352180920,1736103460,8525167680,41741310400,203929367040,

%U 994680578505,4845761001756,23586190895078,114731538098100,557859491227841

%N Catafusenes (see reference for precise definition).

%C The sequence without the initial 0's is the 4-fold convolution of A002212(n), n = 1,2,... . - _Emeric Deutsch_, Mar 13 2004

%C The 2-fold convolution of A045445 (apart from zeros). - _R. J. Mathar_, Aug 01 2019

%H S. J. Cyvin, B. N. Cyvin, J. Brunvoll, and E. Brendsdal, <a href="https://doi.org/10.1021/ci00021a026">Enumeration and classification of certain polygonal systems representing polycyclic conjugated hydrocarbons: annelated catafusenes</a>, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180; see Table 4 (p. 1177).

%H Asamoah Nkwanta, <a href="https://bookstore.ams.org/dimacs-34/">Lattice paths and RNA secondary structures</a>, DIMACS Series in Discrete Math. and Theoretical Computer Science, 34, 1997, 137-147.

%H Asamoah Nkwanta, <a href="http://dimacs.rutgers.edu/archive/Workshops/Diseases/slides/nkwanta.ppt ">Predicting RNA secondary structures: A lattice walk approach to modeling sequences within the HIV-1 RNA structure</a>, slides of a talk given in Johannesburg, South Africa, 2006. [The slides may not necessarily contain this sequence, but they give the background for the above paper in the DIMACS book.]

%F G.f.: (z*M)^4, where M = (1 - 3*z - sqrt(1-6*z+5*z^2))/(2*z^2). - _Emeric Deutsch_, Mar 13 2004

%F a(n) ~ 2 * 5^(n + 1/2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, May 29 2022

%Y Cf. A002212, A004148, A045445.

%K nonn

%O 1,5

%A _N. J. A. Sloane_

%E More terms from _Emeric Deutsch_, Mar 13 2004