OFFSET
0,3
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).
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)
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 *)
PROG
(PARI) a(n)=12*n*(n-1) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Sep 22 2001
STATUS
approved