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%I #61 Nov 20 2020 20:45:06
%S 1,3,4,13,31,109,372,1446,5714,23791,100827,438019,1931818,8648820,
%T 39178079,179383748,828905252,3861958783,18125392905,85631735301,
%U 406977645228,1944737525915,9338989516911,45051405221284,218236995129380,1061256971559421
%N Number of stereoisomers of acyclic hydrocarbons with n carbon atoms.
%C Comment from _Sean A. Irvine_, edited by _Natan Arie Consigli_, Dec 26 2016 : (Start)
%C This is the counting series for the hypothetical stereo-isomers of all acyclic hydrocarbons that satisfy the octet rule.
%C A036673 is the variant with triple bonds excluded.
%C A002986 doesn't count stereoisomers.
%C 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.
%C (End)
%C Read has incorrect a(10)=27100. - _Sean A. Irvine_, Nov 20 2020
%H Sean A. Irvine, <a href="/A036672/a036672.pdf">Correction of A036672(10) and A036673(10)</a>, 2020
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a036/A036672.java">Java program</a> (github)
%H R. C. Read, <a href="/A000598/a000598.pdf">The Enumeration of Acyclic Chemical Compounds</a>, pp. 25-61 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976. [Annotated scanned copy] See p. 60.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Stereoisomerism">Stereoisomerism</a>
%e From _M. F. Hasler_, Dec 26 2016: (Start)
%e For n = 1, there is only a(1) = 1 possibility, CH4.
%e 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.
%e 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)
%e From _Natan Arie Consigli_, Dec 26 2016: (Start)
%e 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.
%e For n = 5 we have:
%e - 3 alkanes: pentane, methylbutane and neopentane.
%e - 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.
%e -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)
%Y Cf. A000598-A000628, A002986, A010372, ..., A086194, ... A134818, ..., A173289, ..., A261336.
%Y Cf. A107984, A036673.
%K nonn
%O 1,2
%A _N. J. A. Sloane_
%E a(10) corrected and more terms from _Sean A. Irvine_, Nov 20 2020
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