A000650 Number of alkyls S C_{n+4} H_{2n+4} with n carbon atoms. (Formerly M1588 N0618)

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

Offset

0,2

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

T. D. Noe, Table of n, a(n) for n=0..200

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; last line of Table I.

G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, last line. (Annotated scanned copy)

Formula

G.f.: A(x) = (r(x)^4+r(x^2)^2)/2, r(x) = A000598(x).

Mathematica

terms = 29; (* r = g.f. of A000598 *) r[_] = 0; Do[r[x_] = 1 + (1/6)*x*(r[x]^3 + 3*r[x]*r[x^2] + 2*r[x^3]) + O[x]^terms // Normal, terms];
A[x_] = (r[x]^4 + r[x^2]^2)/2 + O[x]^terms;
CoefficientList[A[x], x] (* Jean-François Alcover, Jan 25 2012, updated Jan 10 2018 *)

Crossrefs

Sequence in context: A322804 A163087 A332654 * A304961 A032178 A102881

Adjacent sequences: A000647 A000648 A000649 * A000651 A000652 A000653

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved