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Search: id:A002216
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| A002216 |
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Harary-Read numbers: restricted hexagonal polyominoes (cata-polyhexes) with n cells.
(Formerly M1426 N0562)
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+0
8
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| 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)
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OFFSET
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0,4
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REFERENCES
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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. 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.
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LINKS
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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
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FORMULA
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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
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CROSSREFS
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Cf. A036359, A005963, A000228, A001998.
Cf. A002212, A002213, A002214, A002215.
Adjacent sequences: A002213 A002214 A002215 this_sequence A002217 A002218 A002219
Sequence in context: A038142 A052302 A009598 this_sequence A024717 A003724 A138314
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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