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

0,4

Links

Table of n, a(n) for n=0..23.

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

Crossrefs

Cf. A002212 (U), A055879 (V).

Sequence in context: A282857 A296573 A180147 * A378687 A255284 A005825

Adjacent sequences: A044046 A044047 A044048 * A044050 A044051 A044052

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, May 02 2004

Status

approved