A002215 Number of polyhexes with n hexagons, having reflectional symmetry (see Harary and Read for precise definition).

1, 1, 2, 3, 6, 10, 20, 36, 72, 137, 274, 543, 1086, 2219, 4438, 9285, 18570, 39587, 79174, 171369, 342738, 751236, 1502472, 3328218, 6656436, 14878455, 29756910, 67030785, 134061570, 304036170, 608072340, 1387247580, 2774495160

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..200.
• J. Brunvoll, S. J. Cyvin, and B. N. Cyvin, Isomer enumeration of polygonal systems..., J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 10.
• F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.

Crossrefs

Cf. A002212.

Formula

From Emeric Deutsch, Mar 14 2004: (Start)

G.f.: z + (1+2*z)*U(z^2) where U(z) = (1 - 3*z - sqrt(1-6*z+5*z^2))/(2*z) (eq. (16) in the Harary-Read paper).

a(2n) = A002212(n), n >= 1; a(2n+1) = 2*A002212(n), n >= 1. (End)

Extensions

More terms from Emeric Deutsch, Mar 14 2004