A044047 Catafusenes (see reference for precise definition).

0, 0, 0, 1, 2, 12, 56, 282, 1365, 6666, 32002, 153350, 731156, 3480594, 16546884, 78644579, 373813930, 1777680136, 8459543997, 40290717546, 192072529566, 916541991433, 4378019950311, 20933668637794, 100196639221232

Offset

0,5

Links

Table of n, a(n) for n=0..24.

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.

F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.

Formula

G.f.: (1/2)*U(z^2)*V(z) + (1/6)*U(z)^3 + (1/3)*U(z^3) where U(z) = (1 - 3z - sqrt(1 - 6z + 5z^2))/(2z) and V(z) = (1 - z^2 - sqrt(1 - 6z^2 + 5z^4))/(2*z*(1-z)) (eq. (26) in the Cyvin et al. paper).

Crossrefs

Sequence in context: A247121 A078543 A084128 * A296944 A105487 A098453

Adjacent sequences: A044044 A044045 A044046 * A044048 A044049 A044050

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 14 2004

Status

approved