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%I M0772 N0295 #23 Oct 14 2023 23:50:16
%S 1,1,2,3,6,10,20,36,72,137,274,543,1086,2219,4438,9285,18570,39587,
%T 79174,171369,342738,751236,1502472,3328218,6656436,14878455,29756910,
%U 67030785,134061570,304036170,608072340,1387247580,2774495160
%N Number of polyhexes with n hexagons, having reflectional symmetry (see Harary and Read for precise definition).
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A002215/b002215.txt">Table of n, a(n) for n = 1..200</a>.
%H J. Brunvoll, S. J. Cyvin, and B. N. Cyvin, <a href="http://dx.doi.org/10.1016/0166-1280(95)04463-9">Isomer enumeration of polygonal systems...</a>, J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 10.
%H F. Harary and R. C. Read, <a href="https://doi.org/10.1017/S0013091500009135">The enumeration of tree-like polyhexes</a>, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
%F From _Emeric Deutsch_, Mar 14 2004: (Start)
%F 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).
%F a(2n) = A002212(n), n >= 1; a(2n+1) = 2*A002212(n), n >= 1. (End)
%Y Cf. A002212.
%K nonn
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, Mar 14 2004