A000635 Number of paraffins C_n H_{2n} X Y with n carbon atoms.

0, 1, 2, 5, 12, 31, 80, 210, 555, 1479, 3959, 10652, 28760, 77910, 211624, 576221, 1572210, 4297733, 11767328, 32266801, 88594626, 243544919, 670228623, 1846283937, 5090605118, 14047668068, 38794922293, 107215238057, 296501478704

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• 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

• T. D. Noe, Table of n, a(n) for n = 0..200
• Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules
• H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
• H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
• G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I line 3.
• G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 3. (Annotated scanned copy)
• 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. [Annotated scanned copy] See p. 28.

Programs

Mathematica

terms = 29; B[] = 0; Do[B[x] = 1 + (1/6)*x*(B[x]^3 + 3*B[x]*B[x^2] + 2*B[x^3]) + O[x]^terms // Normal, terms];
B642[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;
A[x_] = B642[x]/(1 - B642[x]);
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 21 2011, updated Jan 10 2018 *)

Formula

G.f.: A(x) = B(x)/(1-B(x)), B(x) = g.f. for A000642.