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A000650
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Number of alkyls S C_{n+4} H_{2n+4} with n carbon atoms.
(Formerly M1588 N0618)
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1
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1, 2, 6, 12, 31, 72, 178, 430, 1071, 2654, 6680, 16858, 42926, 109778, 282490, 730028, 1895456, 4940094, 12923600, 33919416, 89301052, 235762572, 624057892, 1655817422, 4403189781, 11733247076, 31326037116, 83786187152, 224475807465
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OFFSET
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0,2
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REFERENCES
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G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; last line of Table I.
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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T. D. Noe, Table of n, a(n) for n=0..200
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FORMULA
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G.f.: A(x) = (r(x)^4+r(x^2)^2)/2, r(x) = A000598(x).
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MATHEMATICA
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max = 28; r[x_] := Sum[ c[k] x^k, {k, 0, max}]; c[0] = c[1] = c[2] = 1; sec = Series[ r[x] - (1 + (x/6)*(r[x]^3 + 3*r[x]*r[x^2] + 2*r[x^3])), {x, 0, max}]; solc = SolveAlways[ Normal[sec] == 0, x]; f[x_] := Sum[ a[k]*x^k, {k, 0, max}]; a[0] = 1; sea = Series[ f[x] - (r[x]^4 + r[x^2]^2)/2, {x, 0, max}]; sola = SolveAlways[ Normal[sea] == 0 /. solc[[1]], x]; A000650 = Table[ a[n] /. sola[[1]], {n, 0, max}] (* From Jean-François Alcover, Jan 25 2012, after g.f. *)
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CROSSREFS
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Sequence in context: A073949 A080372 A163087 * A032178 A102881 A217447
Adjacent sequences: A000647 A000648 A000649 * A000651 A000652 A000653
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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