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A002216 Harary-Read numbers: restricted hexagonal polyominoes (cata-polyhexes) with n cells.
(Formerly M1426 N0562)
11
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; refs; listen; history; text; internal format)
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. 379-390, 1983.

LINKS

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

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

R. C. Read, Letter to N. J. A. Sloane, Feb 12 1971 (includes 40 terms of A002212 and A002216)

Eric Weisstein's World of Mathematics, Polyhex.

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, Dec 23 2003

a(n) ~ 5^(n+1/2)/(4*sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, Aug 09 2013

MATHEMATICA

CoefficientList[Series[(12+(1-5*x)^(3/2)*(1-x)^(3/2)+24*x-48*x^2- 24*x^3- 3*(3+5 x)*Sqrt[1-5*x^2]*Sqrt[1-x^2]-4*Sqrt[1-5*x^3]*Sqrt[1-x^3])/ (24*x^2), {x, 0, 40}], x] (* Harvey P. Dale, Dec 23 2013 *)

CROSSREFS

Cf. A036359, A005963, A000228, A001998.

Cf. A002212, A002213, A002214, A002215.

Sequence in context: A052302 A280275 A009598 * A024717 A003724 A138314

Adjacent sequences:  A002213 A002214 A002215 * A002217 A002218 A002219

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 21 17:52 EDT 2018. Contains 316427 sequences. (Running on oeis4.)