A060785 a(n) = 3*(n - 2)*(5*n -11).

0, 12, 54, 126, 228, 360, 522, 714, 936, 1188, 1470, 1782, 2124, 2496, 2898, 3330, 3792, 4284, 4806, 5358, 5940, 6552, 7194, 7866, 8568, 9300, 10062, 10854, 11676, 12528, 13410, 14322, 15264, 16236, 17238, 18270, 19332, 20424, 21546, 22698, 23880, 25092, 26334

Offset

2,2

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, pp. 313-455.

H. Brocard and T. Lemoyne, Courbes géométriques remarquables (courbes spéciales) Planes et Gauches, Tome I, Paris: Albert Blanchard, 1967 [First publ. 1919]; see p. 135.

Links

Harry J. Smith, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 30*n + a(n-1) - 78 with n>2, a(2)=0. - Vincenzo Librandi, Aug 07 2010

G.f.: 6*x^3*(2+3*x)/(1-x)^3. - Colin Barker, Feb 28 2012

Sum_{n>=3} 1/a(n) = sqrt(5)*log(phi)/6 - tan(3*Pi/10)*Pi/6 + 5*log(5)/12, where phi is the golden ratio (A001622). - Amiram Eldar, Jun 20 2026

Sum_{n>=3} (-1)^(n+1)/a(n) = (Pi*sqrt(phi)/5^(1/4) - 2*log(2) - sqrt(5)*log(phi))/3. - Vaclav Kotesovec, Jun 20 2026

Mathematica

Table[3(n-2)(5n-11), {n, 2, 50}] (* Harvey P. Dale, May 24 2023 *)
(* Alternative: *)
LinearRecurrence[{3, -3, 1}, {0, 12, 54}, 50] (* Harvey P. Dale, May 24 2023 *)

Prog

(PARI) a(n) = 3*(n - 2)*(5*n - 11) \\ Harry J. Smith, Jul 11 2009

Crossrefs

Cf. A001622.

Sequence in context: A341558 A022704 A372025 * A059986 A088941 A019582

Adjacent sequences: A060782 A060783 A060784 * A060786 A060787 A060788

Keyword

nonn,easy

Author

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Apr 28 2001

Status

approved