A044049 Catafusenes (see reference for precise definition).
0, 0, 1, 7, 31, 139, 609, 2677, 11827, 52648, 236071, 1065774, 4841428, 22115678, 101531221, 468224323, 2168076055, 10076177264, 46986612235, 219777649588, 1030892581741, 4848039893338, 22853638285655, 107970202258065
Offset: 0
Keywords
Links
- S. J. Cyvin et al., Enumeration and Classification of Certain Polygonal Systems Representing Polycyclic Conjugated Hydrocarbons: Annelated Catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
Formula
G.f.: (U(z) + V(z) + U(z)^2 + U(z^2) - U(z^2)*V(z) + V(z^3))/2 + (U(z)^3 - U(z^3))/6 - V(z)/z + 1, where U(z) = (1 - 3*z - sqrt(1-6*z+5*z^2)) / (2*z) and V(z) = (1 - z^2 - sqrt(1-6*z^2+5*z^4)) / (2*z*(1-z)) (from eq. (26)-(29) of the Cyvin et al. paper). - Emeric Deutsch, May 02 2004
Extensions
More terms from Emeric Deutsch, May 02 2004