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 A000650 Number of alkyls S C_{n+4} H_{2n+4} with n carbon atoms. (Formerly M1588 N0618) 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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). LINKS T. D. Noe, Table of n, a(n) for n=0..200 FORMULA G.f.: A(x) = (r(x)^4+r(x^2)^2)/2, r(x) = A000598(x). MATHEMATICA 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. *) CROSSREFS Sequence in context: A073949 A080372 A163087 * A032178 A102881 A217447 Adjacent sequences:  A000647 A000648 A000649 * A000651 A000652 A000653 KEYWORD nonn,easy,nice AUTHOR STATUS approved

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