A000648 - OEIS

%I M3045 N1235 #21 Dec 19 2021 09:41:37

%S 1,3,18,61,225,716,2272,6826,20238,58552,167625,473929,1330490,

%T 3709591,10296336,28466065,78481065,215878221,592832960,1625887129,

%U 4454936029,12198071235,33383810793,91336813784,249851178964,683421422654

%N Number of alkyls C_{n+15} H_{2n+10} (Anthr.) with n carbon atoms.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. Polya, <a href="http://dx.doi.org/10.1524/zkri.1936.93.1.415">Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen</a>, Zeit. f. Kristall., 93 (1936), 415-443; line 15 of Table I.

%H G. Polya, <a href="/A000598/a000598_3.pdf">Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen</a>,  Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 15. (Annotated scanned copy)

%F G.f.: A(x) = (r(x)^10 + r(x)^2*r(x^2)^4 + 2*r(x^2)^5)/4, r(x) = A000598(x).

%t terms = 26; (* r = g.f. for 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];

%t A[x_] = (r[x]^10 + r[x]^2*r[x^2]^4 + 2*r[x^2]^5)/4 + O[x]^terms;

%t CoefficientList[A[x], x] (* _Jean-François Alcover_, Jan 10 2018 *)

%Y Cf. A000649.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_