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A000635
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Number of paraffins C_n H_{2n} X Y with n carbon atoms.
(Formerly M1418 N0555)
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1
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0, 1, 2, 5, 12, 31, 80, 210, 555, 1479, 3959, 10652, 28760, 77910, 211624, 576221, 1572210, 4297733, 11767328, 32266801, 88594626, 243544919, 670228623, 1846283937, 5090605118, 14047668068, 38794922293, 107215238057, 296501478704
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| H. R. Henze and C. M. Blair, The number of structural isomers of the more important types of aliphatic compounds, J. Amer. Chem. Soc., 56 (1934), 157.
G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I line 3.
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; see p. 28.
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
| T. D. Noe, Table of n, a(n) for n=0..200
Frederic Chyzak, Enumerating alcohols and other classes of chemical molecules
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FORMULA
| G.f.: A(x) = B(x)/(1-B(x)), B(x) = g.f. for A000642.
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MATHEMATICA
| (* f = gf(A000635), g = gf(A000642), h = gf(A000598) *)
max = 28; f[x_] = Sum[cf[k]*x^k, {k, 0, max}]; g[x_] = Sum[cg[k]*x^k, {k, 0, max}]; h[x_] = Sum[ch[k]*x^k, {k, 0, max}]; coes[k_] := {cf[k], cg[k], ch[k]}; sh = CoefficientList[ Series[ 1 + (1/6)*x*(h[x]^3 + 3*h[x]*h[x^2] + 2*h[x^3]) - h[x], {x, 0, max}], x]; sg = CoefficientList[ Series[ (1/2)*x*(h[x^2] + h[x]^2) - g[x], {x, 0, max}], x]; sf = CoefficientList[ Series[ g[x]/(1 - g[x]) - f[x], {x, 0, max}], x]; eqns = Transpose[ {Thread[sf == 0], Thread[sg == 0], Thread[sh == 0]}]; s[0] = Solve[ eqns[[1]], coes[0]]; Do[eqns = Rest[ eqns /. First[s[k]] ]; s[k+1] = Solve[eqns[[1]], coes[k+1]], {k, 0, max-1}]; Table[ cf[k], {k, 0, max}] /. Flatten[ Table[s[k], {k, 0, max}]] (* From Jean-François Alcover, Oct 21 2011, after g.f. *)
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CROSSREFS
| Sequence in context: A125023 A129804 A110035 * A077556 A097893 A093379
Adjacent sequences: A000632 A000633 A000634 * A000636 A000637 A000638
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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