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A000639 Number of alkyl benzenes with n carbon atoms: C(n)H(2n-6).
(Formerly M3341 N1344)
2
0, 0, 0, 0, 0, 1, 1, 4, 8, 22, 51, 136, 335, 871, 2217, 5749, 14837, 38636, 100622, 263381, 690709, 1817544, 4793449, 12675741, 33592349, 89223734, 237455566, 633176939, 1691377956, 4525792533, 12129365576, 32556355947, 87508275471, 235529797422 (list; graph; refs; listen; history; text; internal format)
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
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
Cf. A000598 (Alkyl radicals).
Sequence in context: A048657 A322284 A175655 * A190795 A052528 A058855
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
Better description from Bruce Corrigan (scentman(AT)myfamily.com), Oct 23 2002
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)