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A002215
Number of polyhexes with n hexagons, having reflectional symmetry (see Harary and Read for precise definition).
(Formerly M0772 N0295)
4
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
1,3
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
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.
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)
CROSSREFS
Cf. A002212.
Sequence in context: A120421 A005418 A329699 * A007562 A345973 A329702
KEYWORD
nonn
EXTENSIONS
More terms from Emeric Deutsch, Mar 14 2004
STATUS
approved