login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000642 a(1)=0; for n>1, a(n) = number of isomeric hydrocarbons of the acetylene series with carbon content n.
(Formerly M0839 N0318)
12
0, 1, 1, 2, 3, 7, 14, 32, 72, 171, 405, 989, 2426, 6045, 15167, 38422, 97925, 251275, 648061, 1679869, 4372872, 11428365, 29972078, 78859809, 208094977, 550603722, 1460457242, 3882682803, 10344102122, 27612603765, 73844151259, 197818389539 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The former definition was "Number of alkyl derivatives of acetylene X^{II} C_n H_{2n+2} with n carbon atoms" with offset 0.

REFERENCES

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..201 (offset adapted by Georg Fischer, Jan 31 2019)

D. D. Coffman, C. M. Blair and H. R. Henze, The number of structurally isomeric hydrocarbons of the acetylene series, J. Amer. Chem. Soc., 55 (1933), 252-253.

D. D. Coffman, C. M. Blair and H. R. Henze, The number of structurally isomeric hydrocarbons of the acetylene series, J. Amer. Chem. Soc., 55 (1933), 252-253. (Annotated scanned copy)

Jean-Loup Faulon, Donald P. Visco Jr., Diana Roe, Enumerating Molecules, In: Reviews in Computational Chemistry Vol. 21, Ed. K. Lipkowitz, Wiley-VCH, 2005.

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 8 of Table I, "R" of Table IV.

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen,  Zeit. f. Kristall., 93 (1936), 415-443; line 8 of Table I, "R" of Table IV. (Annotated scanned copy)

R. C. Read, Some recent results in chemical enumeration, Lect. Notes Math. 303 (1972), 243-259.

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.

N. Trinajstich, Z. Jerievi, J. V. Knop, W. R. Muller and K. Szymanski, Computer Generation of Isomeric Structures, Pure & Appl. Chem., Vol. 55, No. 2, pp. 379-390, 1983.

FORMULA

G.f.: A(x)=(1/2)*x*(B(x^2)+B(x)^2), where B(x) = g.f. for A000598.

a(n) ~ c * d^n / n^(3/2), where d = 1/A261340 = 2.815460033176... and c = 0.13833565403175156418512996853... - Vaclav Kotesovec, Feb 11 2019

MATHEMATICA

terms = 32; 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];

A[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;

CoefficientList[A[x], x] (* Jean-Fran├žois Alcover, Jun 28 2012, updated Jan 10 2018 *)

CROSSREFS

Cf. A002094.

Sequence in context: A205484 A151530 A180752 * A229734 A035083 A328057

Adjacent sequences:  A000639 A000640 A000641 * A000643 A000644 A000645

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

I changed the definition and offset so as to agree with Coffman et al. (1933). - N. J. A. Sloane, Jan 13 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 12:35 EST 2019. Contains 329261 sequences. (Running on oeis4.)