cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Previous Showing 11-14 of 14 results.

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

Original entry on oeis.org

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

Views

Author

Keywords

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

Examples

			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

Extensions

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

A036673 Number of stereoisomers of all n-node acyclic hydrocarbons with no triple bonds.

Original entry on oeis.org

1, 2, 3, 9, 20, 64, 205, 747, 2767, 10850, 43254, 176990, 735007, 3099272, 13220407, 57001841, 248009246, 1087947441, 4807232915, 21381055533, 95660032110, 430298114499, 1945096434552, 8832200860663, 40271358004756, 184325394540531, 846667179332120
Offset: 1

Views

Author

Keywords

Comments

Alternatively, unrooted steric quartic trees allowing single and double edges with n nodes. - Natan Arie Consigli, Jun 30 2017
Read has incorrect a(10)=14159. - Sean A. Irvine, Nov 20 2020

Crossrefs

Cf. A000628 (steric quartic trees with no double edges).

Extensions

Name clarified by Natan Arie Consigli, Jun 30 2017
a(10) corrected and more terms from Sean A. Irvine, Nov 20 2020

A005630 Number of chiral trees with n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 4, 10, 34, 96, 284, 782, 2226, 6208, 17560, 49618, 141500, 405104, 1168316, 3386538, 9875232, 28939944, 85235762, 252159572, 749160544, 2234378156, 6688358338, 20088296030, 60524845158, 182893018756
Offset: 1

Views

Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Formula

a(n) = A000628(n) - A005629(n). - Emeric Deutsch, Nov 21 2004

Extensions

Corrected and extended by Emeric Deutsch, Nov 21 2004

A280006 Number of possible connected steric graphs with n nodes of degree less than 5, excluding the ones with all nodes of degree 4 and trees.

Original entry on oeis.org

0, 0, 1, 6, 39, 399
Offset: 1

Views

Author

Natan Arie Consigli, Jan 02 2017

Keywords

Comments

Also number of hypothetical neutrally charged hydrocarbons with n carbon atoms containing a cyclic set of atoms (cycloalkanes and alkyl-cycloalkanes) satisfying the octet rule. This includes all isomers except conformers.
Steric (three-dimensional) graphs can be represented as two-dimensional graphs provided that stereoisomers are taken into account. This means acting the group S_4 on the stereocenters (nodes with 4 different substituents) of each 2D graph and counting all of the resulting non-symmetric molecules.
The terms of this sequence (and related ones) were found by drawing and counting the hydrocarbons in the PDFs below. If there are any missing molecules you can contact me. I'll add them in the PDF and update the data section.
Many of those "theoretical" molecules are to be discovered and some may not exist due to their strained geometries.

Crossrefs

Cf. A000628 (counts acyclic alkanes), A000639 (counts alkyl-benzenes).

Formula

a(n) = A280012(n) - A000628(n).
Previous Showing 11-14 of 14 results.