A002215 Number of polyhexes with n hexagons, having reflectional symmetry (see Harary and Read for precise definition). (Formerly M0772 N0295)

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

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.

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)

D-finite with recurrence (n+2)*a(n) +2*(n)*a(n-1) +6*(-n+1)*a(n-2) +12*(-n+3)*a(n-3) +5*(n-4)*a(n- 4) +10*(n-6)*a(n-5)=0. - R. J. Mathar, Mar 02 2026

Crossrefs

Cf. A002212.

Sequence in context: A120421 A005418 A329699 * A007562 A345973 A329702

Adjacent sequences: A002212 A002213 A002214 * A002216 A002217 A002218

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, Mar 14 2004

Status

approved