A045829 Catafusenes (see reference for precise definition).

0, 0, 0, 1, 12, 94, 612, 3605, 19992, 106644, 554184, 2827902, 14244120, 71073860, 352180920, 1736103460, 8525167680, 41741310400, 203929367040, 994680578505, 4845761001756, 23586190895078, 114731538098100, 557859491227841

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

The 2-fold convolution of A045445 (apart from zeros). - R. J. Mathar, Aug 01 2019

Links

• S. J. Cyvin, B. N. Cyvin, J. Brunvoll, and E. Brendsdal, Enumeration and classification of certain polygonal systems representing polycyclic conjugated hydrocarbons: annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180; see Table 4 (p. 1177).
• Asamoah Nkwanta, Lattice paths and RNA secondary structures, DIMACS Series in Discrete Math. and Theoretical Computer Science, 34, 1997, 137-147.
• Asamoah Nkwanta, Predicting RNA secondary structures: A lattice walk approach to modeling sequences within the HIV-1 RNA structure, 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.]

Crossrefs

Cf. A002212, A004148, A045445.

Formula

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

a(n) ~ 2 * 5^(n + 1/2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, May 29 2022

Extensions

More terms from Emeric Deutsch, Mar 13 2004