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A000639 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

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-Fran├žois Alcover, Oct 12 2011, updated Nov 24 2016 *)

CROSSREFS

Cf. A000598 (Alkyl radicals).

Sequence in context: A048657 A322284 A175655 * A190795 A052528 A058855

Adjacent sequences:  A000636 A000637 A000638 * A000640 A000641 A000642

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

Better description from Bruce Corrigan (scentman(AT)myfamily.com), Oct 23 2002

STATUS

approved

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Last modified November 12 04:21 EST 2019. Contains 329051 sequences. (Running on oeis4.)