A064200 a(n) = 12*n*(n-1).

0, 0, 24, 72, 144, 240, 360, 504, 672, 864, 1080, 1320, 1584, 1872, 2184, 2520, 2880, 3264, 3672, 4104, 4560, 5040, 5544, 6072, 6624, 7200, 7800, 8424, 9072, 9744, 10440, 11160, 11904, 12672, 13464, 14280, 15120, 15984, 16872, 17784, 18720, 19680, 20664, 21672

Offset: 0

Author

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Sep 22 2001

Keywords

• nonn
• easy

References

• Luigi Berzolari, Allgemeine Theorie der Höheren Ebenen Algebraischen Kurven, Encyclopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Band III_2, Heft 3, Leipzig: B. G. Teubner, 1906, p. 341.

Links

• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets.
• Leo Tavares, Illustration: Twin Stars.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A262221, A003154.

Programs

Mathematica

Table[12n(n-1),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{0,0,24},40] (* Harvey P. Dale, Jul 22 2015 *)
Join[{0},24*Accumulate[Range[0,60]]] (* Harvey P. Dale, Dec 17 2022 *)

PARI

a(n)=12*n*(n-1) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = 24*(n-1) + a(n-1) for n>0, with a(0)=0. - Vincenzo Librandi, Aug 07 2010

a(0)=0, a(1)=0, a(2)=24, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Jul 22 2015

G.f.: -(24*x^2)/(x-1)^3. - Harvey P. Dale, Jul 22 2015

a(n) = 2*A003154(n) - 2. See Twin Stars illustration. - Leo Tavares, Aug 23 2021

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=2} 1/a(n) = 1/12.

Sum_{n>=2} (-1)^n/a(n) = (2*log(2) - 1)/12.

Product_{n>=2} (1 - 1/a(n)) = -(12/Pi)*cos(Pi/sqrt(3)).

Product_{n>=2} (1 + 1/a(n)) = (12/Pi)*cos(Pi/sqrt(6)). (End)