A036672 Number of stereoisomers of acyclic hydrocarbons with n carbon atoms.

1, 3, 4, 13, 31, 109, 372, 1446, 5714, 23791, 100827, 438019, 1931818, 8648820, 39178079, 179383748, 828905252, 3861958783, 18125392905, 85631735301, 406977645228, 1944737525915, 9338989516911, 45051405221284, 218236995129380, 1061256971559421

Offset

1,2

Comments

Comment from Sean A. Irvine, edited by Natan Arie Consigli, Dec 26 2016 : (Start)

This is the counting series for the hypothetical stereo-isomers of all acyclic hydrocarbons that satisfy the octet rule.

A036673 is the variant with triple bonds excluded.

A002986 doesn't count stereoisomers.

The reference gives a three-variable generating function and cycle-index over A4 which can produce both these sequences. There are also dependencies on earlier generating functions.

(End)

Read has incorrect a(10)=27100. - Sean A. Irvine, Nov 20 2020

Links

Table of n, a(n) for n=1..26.

Sean A. Irvine, Correction of A036672(10) and A036673(10), 2020

Sean A. Irvine, Java program (github)

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. 60.

Wikipedia, Stereoisomerism

Example

From M. F. Hasler, Dec 26 2016: (Start)
For n = 1, there is only a(1) = 1 possibility, CH4.
For n = 2, one has C2H6 (ethane, H3C-CH3), C2H4 (ethylene, H2C=CH2 with a double bond), C2H2 (ethyne, HC≡CH, triple bond), whence a(2) = 3.
For n = 3, one has C3H8 (H3C-CH2-CH3), C3H6 (H2C=CH-CH3, propene), and two C3H4 (H2C=C=CH2, propadiene, and HC≡C-CH3: methylacetylene), thus a(3) = 4. Cyclic molecules like cyclopropane C3H6 and cyclopropropene C3H4 are excluded. (End)
From Natan Arie Consigli, Dec 26 2016: (Start)
For n = 4, we have butane, isobutane, 1-butene, cis/trans-2-butene, buta-1,2-diene, buta-1,3-diene, butatriene, isobutylene, but-1-yne, but-2-yne, diacetylene, but-1-en-3-yne.
For n = 5 we have:
- 3 alkanes: pentane, methylbutane and neopentane.
- 17 alkenes: 1-pentene, (E/Z)-2-pentene, 1,2-pentadiene, (E/Z)-1,3-pentadiene, 1,4-pentadiene, 1,2,3-petatriene, penta-1,2,4-triene, pentatetraene, 2-methylbut-1-ene, 2-methylbut-2-ene, 3-methylbut-1-ene, isoprene, 3-methylbuta-1,2-diene, (R/S)-penta-2,3-diene.
-11 alkynes: 1-pentyne, 2-pentyne, pent-1-en-4-yne, (E/Z)-pent-3-en-1-yne, penta-1,2-dien-4-yne, penta-1,4-diyne, penta-1,3-diyne, pent-1-en-3-yne, 3-methylbut-1-yne, 2-methylbut-1-en-3-yne. (End)

Crossrefs

Cf. A000598-A000628, A002986, A010372, ..., A086194, ... A134818, ..., A173289, ..., A261336.

Cf. A107984, A036673.

Sequence in context: A142860 A111954 A192872 * A174684 A286917 A084315

Adjacent sequences: A036669 A036670 A036671 * A036673 A036674 A036675

Keyword

nonn

Author

N. J. A. Sloane

Extensions

a(10) corrected and more terms from Sean A. Irvine, Nov 20 2020

Status

approved