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A002216 Harary-Read numbers: restricted hexagonal polyominoes (cata-polyhexes) with n cells.
(Formerly M1426 N0562)
+0
8
0, 1, 1, 2, 5, 12, 37, 123, 446, 1689, 6693, 27034, 111630, 467262, 1981353, 8487400, 36695369, 159918120, 701957539, 3101072051, 13779935438, 61557789660, 276327463180, 1245935891922, 5640868033058, 25635351908072, 116911035023017 (list; graph; listen)
OFFSET

0,4

REFERENCES

L. W. Beineke and R. E. Pippert, On the enumeration of planar trees of hexagons, Glasgow Math. J., 15 (1974), 131-147.

S. J. Cyvin et al., Number of perifusenes with one internal vertex, Rev. Roumaine Chem., 38 (1993), 65-77.

S. J. Cyvin et al., Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), 55-70.

J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.

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

J. V. Knop et al., On the total number of polyhexes, Match, No. 16 (1984), 119-134.

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).

N. Trinajstich, Z. Jerievi, J. V. Knop, W. R. Muller and K. Szymanski, COMPUTER GENERATION OF ISOMERIC STRUCTURES, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-39O, 1983.

LINKS

T. D. Noe, Table of n, a(n) for n=0..200

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Fusene

FORMULA

G.f.: (1/(24*x^2))*(12+24*x-48*x^2-24*x^3 +(1-x)^(3/2)*(1-5*x)^(3/2)-3*(3+5*x)*(1-x^2)^(1/2)*(1-5*x^2)^(1/2) -4*(1-x^3)^(1/2)*(1-5*x^3)^(1/2)).

a(n)=(1/2)[A002214(n)+A002215(n)], n>=1. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 23 2003

CROSSREFS

Cf. A036359, A005963, A000228, A001998.

Cf. A002212, A002213, A002214, A002215.

Sequence in context: A038142 A052302 A009598 this_sequence A024717 A003724 A138314

Adjacent sequences: A002213 A002214 A002215 this_sequence A002217 A002218 A002219

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified December 17 23:40 EST 2009. Contains 171025 sequences.


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