OFFSET
0,4
COMMENTS
Named after the American mathematician Frank Harary (1921-2005) and the British mathematician Ronald Cedric Read (1924-2019). - Amiram Eldar, Jun 22 2021
REFERENCES
S. J. Cyvin, J. Brunvoll, X. F. Guo and F. J. Zhang, Number of perifusenes with one internal vertex, Rev. Roumaine Chem., Vol. 38, No. 1 (1993), pp. 65-77.
S. J. Cyvin, B. N. Cyvin, and J. Brunvoll, Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem., Vol. 134, No. 1 (1997), pp. 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.
Wenchen He and Wenjie He, Generation and enumeration of planar polycyclic aromatic hydrocarbons, Tetrahedron, Vol. 42, No. 19 (1986), pp. 5291-5299. See Table 3.
J. V. Knop, K. Szymansky, Željko Jeričević and Nenad Trinajstić, On the total number of polyhexes, Match, Vol. 16 (1984), pp. 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 (1983), pp. 379-390.
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., Vol. 15, No. 2 (1974), pp. 131-147.
L. W. Beineke and R. E. Pippert, On the enumeration of planar trees of hexagons, Glasgow Math. J., Vol. 15, No. 2 (1974), pp. 131-147. [Annotated scanned copy]
S. J. Cyvin, J. Brunvoll and B. N. Cyvin, Harary-Read numbers for catafusenes: Complete classification according to symmetry, Journal of mathematical chemistry, Vol. 9, No. 1 (1992), pp. 19-31 and 33-38. See Table 2.
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinb. Math. Soc., Vol. 17, No. 1 (1970), pp. 1-13; alternative link.
J. V. Knop, K. Szymanski, Ž. Jeričević, and N. Trinajstić, On the total number of polyhexes, Match, No. 16 (1984), 119-134.
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) ~ 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
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved