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A000640
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Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms.
(Formerly M3466 N1410)
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2
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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
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OFFSET
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0,3
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REFERENCES
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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).
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LINKS
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FORMULA
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MAPLE
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# 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)];
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MATHEMATICA
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terms = 27; (* B, B2 = g.f. for A000598, A000642 resp. *) 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];
B2[x_] = (1/2)*x*(B[x^2] + B[x]^2) + O[x]^terms;
A[x_] = x*B[x]/(1 - B2[x])^3 + O[x]^terms;
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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