A000635 Number of paraffins C_n H_{2n} X Y with n carbon atoms. (Formerly M1418 N0555)

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

0,3

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.

Formula

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

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 *)

Crossrefs

Sequence in context: A335457 A290616 A110035 * A317098 A238427 A077556

Adjacent sequences: A000632 A000633 A000634 * A000636 A000637 A000638

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved