A000648 Number of alkyls C_{n+15} H_{2n+10} (Anthr.) with n carbon atoms.

1, 3, 18, 61, 225, 716, 2272, 6826, 20238, 58552, 167625, 473929, 1330490, 3709591, 10296336, 28466065, 78481065, 215878221, 592832960, 1625887129, 4454936029, 12198071235, 33383810793, 91336813784, 249851178964, 683421422654

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

• G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; line 15 of Table I.
• G. Polya, Algebraische Berechnung der Anzahl der Isomeren einiger organischer Verbindungen, Zeit. f. Kristall., 93 (1936), 415-443; Table I, line 15. (Annotated scanned copy)

Crossrefs

Cf. A000649.

Programs

Mathematica

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];
A[x_] = (r[x]^10 + r[x]^2*r[x^2]^4 + 2*r[x^2]^5)/4 + O[x]^terms;
CoefficientList[A[x], x] (* Jean-François Alcover, Jan 10 2018 *)

Formula

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