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A036672 Number of stereoisomers of acyclic hydrocarbons with n carbon atoms. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 20 06:56 EDT 2021. Contains 345157 sequences. (Running on oeis4.)