A000632 -id:A000632 - cp's OEIS frontend

A000633 Number of acyclic quaternary ammonium ions with n carbon atoms.

1, 1, 3, 7, 18, 42, 109, 269, 691, 1759, 4542, 11733, 30559, 79743, 209136, 549959, 1451178, 3838925, 10182703, 27069940, 72121696, 192527888, 514908269, 1379454526, 3701556642, 9947456861, 26770280299, 72138803942, 194638086892, 525773470041, 1421850523472

Offset: 4

N. J. A. Sloane

nonn

First page of Henze paper gives a(15)=11733, a(20)=1451178.

Equivalent to the number of rooted trees where the root (the nitrogen atom) has four children and each child is a nonempty unlabeled ternary tree. - Sean A. Irvine, May 21 2023

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).

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
David Consiglio, Jr., Illustration of n=4, 5, and 6
David Consiglio, Jr., Illustration of n=7
David Consiglio, Jr., Illustration of n=8

Cf. A000598.

G.f. A(x) = cycle_index(S4, B(x)-1), where B(x) is g.f. for A000598 and S4 is the symmetric group on 4 elements. - Sean A. Irvine, May 21 2023

Revised by David Consiglio, Jr. and Sean A. Irvine, May 21 2023

A000635 Number of paraffins C_n H_{2n} X Y with n carbon atoms.

Original entry on oeis.org

0, 1, 2, 5, 12, 31, 80, 210, 555, 1479, 3959, 10652, 28760, 77910, 211624, 576221, 1572210, 4297733, 11767328, 32266801, 88594626, 243544919, 670228623, 1846283937, 5090605118, 14047668068, 38794922293, 107215238057, 296501478704

Offset: 0

N. J. A. Sloane

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).

T. D. Noe, Table of n, a(n) for n = 0..200
Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I line 3.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 3. (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.

terms = 29; B[] = 0; Do[B[x] = 1 + (1/6)*x*(B[x]^3 + 3*B[x]*B[x^2] + 2*B[x^3]) + O[x]^terms // Normal, terms];
B642[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;
A[x_] = B642[x]/(1 - B642[x]);
CoefficientList[A[x], x] (* Jean-François Alcover, Oct 21 2011, updated Jan 10 2018 *)

G.f.: A(x) = B(x)/(1-B(x)), B(x) = g.f. for A000642.

A000636 Number of paraffins C_n H_{2n} X_2 with n carbon atoms.

Original entry on oeis.org

1, 2, 4, 9, 21, 52, 129, 332, 859, 2261, 5983, 15976, 42836, 115469, 312246, 847241, 2304522, 6283327, 17164401, 46972357, 128741107, 353345434, 970999198, 2671347292, 7356752678, 20279171785, 55948407837, 154479213626, 426845422807, 1180229767202

Offset: 1

N. J. A. Sloane

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).

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (Annotated scanned copy)
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 4 of Table I.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 2. (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.

G.f.: (1/2) * (1/(1-x*R(x)) + (1+x*R(x)) / (1-x^2*R(x^2))) where R(x) is the g.f. for A000642 [From Polya paper]. - Sean A. Irvine, Oct 04 2016

More terms from Sean A. Irvine, Oct 04 2016

A000634 Number of glycols with n carbon atoms.

Original entry on oeis.org

1, 2, 6, 14, 38, 97, 260, 688, 1856, 4994, 13550, 36791, 100302, 273824, 749316, 2053247, 5635266, 15484532, 42599485, 117312742, 323373356, 892139389, 2463252315, 6806148956, 18818714543, 52065725034, 144135111504, 399232819042, 1106385615943

Offset: 2

N. J. A. Sloane

nonn

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).

H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157.
H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1) (1934), 157-157. (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.

Cf. A000636, A000642.

a(n) = A000636(n) - A000642(n). - Sean A. Irvine, Nov 18 2016

More terms from Sean A. Irvine, Nov 18 2016

cp's OEIS Frontend

A000633 Number of acyclic quaternary ammonium ions with n carbon atoms.

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A000635 Number of paraffins C_n H_{2n} X Y with n carbon atoms.

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A000636 Number of paraffins C_n H_{2n} X_2 with n carbon atoms.

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A000634 Number of glycols with n carbon atoms.

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