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A000640 Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms.
(Formerly M3466 N1410)
2
0, 1, 4, 13, 42, 131, 402, 1218, 3657, 10899, 32298, 95257, 279844, 819390, 2392392, 6967956, 20250974, 58744089, 170118980, 491913999, 1420493862, 4096940530, 11803172152, 33970257473, 97678027311, 280624328431, 805587723862 (list; graph; refs; listen; history; internal format)
OFFSET

0,3

REFERENCES

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443.

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

N. J. A. Sloane, Table of n, a(n) for n = 0..100

Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules

FORMULA

G.f.: A(x) = x*A000598(x)/(1-A000642(x))^3.

MAPLE

The following Maple commands are taken from the Chyzak web site:

with(combstruct);

gramm_Alkyl:=Alkyl=Prod(Carbon, Set(Alkyl, card<=3)), Carbon=Atom:

specs_Alkyl:=[Alkyl, {gramm_Alkyl}, unlabeled]:

gramm_S1_Alkyl:=S1_Alkyl[X]=Union(Prod(Carbon, S1_Alkyl[X], Set(Alkyl, card<=2)), Prod(Prod(Carbon, X), Set(Alkyl, card<=2))), X=Epsilon:

specs_S1_Alkyl:=[S1_Alkyl[X], {gramm_S1_Alkyl, gramm_Alkyl}, unlabeled]:

gramm_S2_Alkyl:=S2_Alkyl[X, Y]=Union(Prod(Carbon, S2_Alkyl[X, Y], Set(Alkyl, card<=2)), Prod(Carbon, Union(S1_Alkyl[X], X), Union(S1_Alkyl[Y], Y), Set(Alkyl, card<=1))):

specs_S2_Alkyl:=[S2_Alkyl[X, Y], {gramm_S2_Alkyl, gramm_S1_Alkyl, op(subs(X=Y, [gramm_S1_Alkyl])), gramm_Alkyl}, unlabeled]:

[seq(count(specs_S2_Alkyl, size=i), i=0..50)];

CROSSREFS

Sequence in context: A186202 A036366 A109454 * A199842 A192910 A010919

Adjacent sequences:  A000637 A000638 A000639 * A000641 A000642 A000643

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified February 17 16:49 EST 2012. Contains 206058 sequences.