OFFSET
1,8
REFERENCES
N. L. Biggs et al., Graph Theory 1736-1936, Oxford, 1976, p. 71.
R. C. Read, The Enumeration of Acyclic Chemical Compounds, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. p. 22, Eq. (H).
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
Vincenzo Librandi, Table of n, a(n) for n = 1..100
I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443 (p. 422).
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443 (p. 422). (Annotated scanned copy)
FORMULA
G.f.: (x^6/12)*(B(x)^6+4*B(x^2)^3+2*B(x^3)^2+3*B(x)^2*B(x^2)^2+2*B(x^6)), where B = g.f. of A000598.
EXAMPLE
G.f. = x^6 + x^7 + 4*x^8 + 8*x^9 + 22*x^10 + 51*x^11 + 136*x^12 + 335*x^13 + ...
a(8)=4 because the unique isomers are 1,2-Dimethylbenzene; 1,3-Dimethylbenzene; 1,4-Dimethylbenzene, 1-Ethylbenzene. All have formula C(8)H(10)
MATHEMATICA
m = 100; For[A = 0; i = 0, i <= m, i++, A = Series[1 + x*(A^3/6 + (A /. x -> x^2)*A/2 + (A /. x -> x^3)/3), {x, 0, m+1}] // Normal]; B[x_] = A; (1/12)*(B[x]^6 + 4*B[x^2]^3 + 2*B[x^3]^2 + 3*B[x]^2*B[x^2]^2 + 2*B[x^6]) + O[x]^m // CoefficientList[#, x]& // Join[{0, 0, 0, 0, 0}, #]& (* Jean-François Alcover, Oct 12 2011, updated Nov 24 2016 *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Better description from Bruce Corrigan (scentman(AT)myfamily.com), Oct 23 2002
STATUS
approved