A000599 Number of secondary alcohols (alkanols or alkyl alcohols C_n H_{2n+1} OH) with n carbon atoms. (Formerly M2585 N1023)

0, 0, 0, 1, 1, 3, 6, 15, 33, 82, 194, 482, 1188, 2988, 7528, 19181, 49060, 126369, 326863, 849650, 2216862, 5806256, 15256265, 40210657, 106273050, 281593237, 747890675, 1990689459, 5309397294, 14187485959, 37977600390, 101827024251

Offset

0,6

References

J. L. Faulon, D. Visco and D. Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.

Handbook of Combinatorics, North-Holland '95, p. 1963.

D. Perry, The number of structural isomers ..., J. Amer. Chem. Soc. 54 (1932), 2918-2920.

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

Seiichi Manyama, Table of n, a(n) for n = 0..1000

H. R. Henze and C. M. Blair, The number of structurally isomeric alcohols of the methanol series, J. Amer. Chem. Soc., 53 (8) (1931), 3042-3046.

H. R. Henze and C. M. Blair, The number of structurally isomeric alcohols of the methanol series, J. Amer. Chem. Soc., 53 (8) (1931), 3042-3045. (Annotated scanned copy)

D. Perry, The number of structural isomers of certain homologs of methane and methanol, J. Amer. Chem. Soc. 54 (1932), 2918-2920. [Gives a(60) correctly] (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, 38 (Q(x)).

N. Trinajstich, Z. Jerievi, J. V. Knop, W. R. Muller and K. Szymanski, Computer Generation of Isomeric Structures, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-390, 1983.

Formula

Henze and Blair give a recurrence.; also g.f. A(x) = x*cycle_index(S2, B(x)-1), where B(x) is g.f. for A000598.

Crossrefs

Cf. A000598, A000600, A000633, A036670.

Sequence in context: A336632 A152167 A105476 * A063832 A006647 A032126

Adjacent sequences: A000596 A000597 A000598 * A000600 A000601 A000602

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(0)=0 prepended by Seiichi Manyama, May 12 2026

Status

approved