A000625 -id:A000625 - cp's OEIS frontend

A005958 Number of esters with n carbon atoms up to stereo-isomerism.

1, 2, 4, 10, 25, 64, 172, 472, 1319, 3750, 10796, 31416, 92276, 273172, 814246, 2441688, 7360877, 22295746, 67819576, 207083944, 634512581, 1950301202, 6011920720, 18581123978, 57568802820, 178763375468, 556255762692, 1734248037856

Offset: 2

N. J. A. Sloane

nonn

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

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. 44.

G.f.: B(x)*(B(x)-1) where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

More terms from Sean A. Irvine, Nov 12 2016

Name clarified by Sean A. Irvine, Feb 01 2025

A005959 Number of acyclic ethylene derivatives with n carbon atoms.

Original entry on oeis.org

1, 1, 4, 6, 18, 42, 118, 314, 895, 2521, 7307, 21238, 62566, 185310, 553288, 1660490, 5011299, 15190665, 46244031, 141296042, 433204573, 1332261200, 4108833222, 12704949506, 39379343929, 122327632914, 380778749899, 1187544117426

Offset: 2

N. J. A. Sloane

nonn

			G.f. = x^2 + x^3 + 4*x^4 + 6*x^5 + 18*x^6 + 42*x^7 + 118*x^8 + 314*X^9 + ...

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

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. 44.

G.f.: (1/4)*x^2*(B(x)^4+3*B(x^2)^2) where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

More terms from Sean A. Irvine, Nov 12 2016

A005962 Number of carbon trees with n carbon atoms.

Original entry on oeis.org

1, 1, 2, 4, 10, 22, 60, 158, 439, 1229, 3525, 10178, 29802, 87862, 261204, 781198, 2350249, 7105081, 21577415, 65787902, 201313311, 618040002, 1903102730, 5876174472, 18189503139, 56435742554, 175477142565, 546703920430, 1706433403626

Offset: 1

N. J. A. Sloane

nonn

Table II in the Read article is missing a(4)=4 and thereafter all entries in the table are off by one position. - Sean A. Irvine, Nov 12 2016

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

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. 44.
Index entries for sequences related to trees

G.f.: x * (B(x)^4 + 3*B(x^2)^2 + 8*B(x)*B(x^3)) / 12 where B(x) is the g.f. for A000625. - Sean A. Irvine, Nov 12 2016

a(4) inserted and more terms from Sean A. Irvine, Nov 12 2016

A055936 Stereoisomeric homologs with molecular formula C_{3+n} H_{6+2n}.

Original entry on oeis.org

1, 1, 5, 11, 33, 87, 259, 730, 2150, 6278, 18622, 55340, 165857, 498907, 1509012, 4581570, 13967031, 42722777, 131110259, 403527667, 1245358416, 3852965298, 11948207174, 37131355170, 115623660978, 360712069084, 1127276560366

Offset: 0

Vladeta Jovovic, Aug 21 2001

nonn

G. Polya and R. C. Read, Combinatorial Enumeration of Groups, Graphs and Chemical Compounds, Springer-Verlag, 1987, pp. 63-64.

G. Polya, Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Math. 68 (1937), 145-254.

Cf. A000625, A063832.

G.f.: A(x) = (B(x)^6 + 3*B(x^2)^3 + 2*B(x^3)^2)/6, where B(x) is g.f. for A000625.

A152081 Least prime divisor of terms of A152080.

Original entry on oeis.org

5, 7, 3, 7, 5, 3, 11, 3, 5, 7, 3, 11, 13, 3, 7, 3, 3, 5, 5, 3, 5, 3, 13, 17, 3, 7, 11, 5, 7, 5, 3, 3, 7, 5, 3, 11, 5, 5, 19, 7, 5, 29, 3, 3, 11, 5, 5, 7, 11, 3, 7, 29, 5, 3, 3, 19, 3, 3, 3, 13, 5, 7, 29, 7, 31, 3, 23, 17, 13, 13, 3, 19, 3, 3, 7, 3, 5, 7, 3, 11, 11, 29, 37

Offset: 1

Vladimir Shevelev, Nov 23 2008

nonn

Cf. A020639, A152080, A000625, A152021, A152022, A152023, A152078.

a000695(n) = fromdigits(binary(n), 4);
lista(nn) = forcomposite(n=1, nn, if (isprime(a000695(n)), print1(factor(n)[1,1], ", "))); \\ Michel Marcus, Dec 18 2018

a(n) = A020639(A152080(n)). - Michel Marcus, Sep 24 2023

More terms from Michel Marcus, Jun 02 2013

More terms from Michel Marcus, Dec 18 2018

cp's OEIS Frontend

A005958 Number of esters with n carbon atoms up to stereo-isomerism.

Views

Author

Keywords

References

Links

Formula

Extensions

A005959 Number of acyclic ethylene derivatives with n carbon atoms.

Views

Author

Keywords

Examples

References

Links

Formula

Extensions

A005962 Number of carbon trees with n carbon atoms.

Views

Author

Keywords

Comments

References

Links

Formula

Extensions

A055936 Stereoisomeric homologs with molecular formula C_{3+n} H_{6+2n}.

Views

Author

Keywords

References

Links

Crossrefs

Formula

A152081 Least prime divisor of terms of A152080.

Views

Author

Keywords

Crossrefs

Programs

PARI

Formula

Extensions