A000640 Number of paraffins C_n H_{2n-1} XYZ with n carbon atoms.
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
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
- N. J. A. Sloane, Table of n, a(n) for n = 0..100
- Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules
- G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443.
- G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443. (Annotated scanned copy)
Programs
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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)]; -
Mathematica
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; CoefficientList[A[x], x] (* Jean-François Alcover, Jan 10 2018 *)