A060787 a(n) = 18*(n - 2)*(2*n - 5).

0, 18, 108, 270, 504, 810, 1188, 1638, 2160, 2754, 3420, 4158, 4968, 5850, 6804, 7830, 8928, 10098, 11340, 12654, 14040, 15498, 17028, 18630, 20304, 22050, 23868, 25758, 27720, 29754, 31860, 34038, 36288, 38610, 41004, 43470, 46008, 48618, 51300, 54054, 56880, 59778

Offset: 2

Author

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

Keywords

• nonn
• easy

Comments

Except for first term Engel expansion of cosh(1/3); cf. A006784 for Engel expansion definition. - Benoit Cloitre, Mar 03 2002

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.
• Henri Brocard and Timoléon 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).

Crossrefs

Cf. A006784.

Programs

Mathematica

a[n_] := 18*(n-2)*(2*n-5); Array[a, 50, 2] (* Amiram Eldar, May 05 2025 *)

PARI

a(n) = 18*(n - 2)*(2*n - 5) \\ Harry J. Smith, Jul 11 2009

Formula

G.f.: 18*x^3*(1 + 3*x)/(1 - x)^3. - Colin Barker, Feb 29 2012

From Amiram Eldar, May 05 2025: (Start)

Sum_{n>=3} 1/a(n) = log(2)/9.

Sum_{n>=3} (-1)^(n+1)/a(n) = Pi/36 - log(2)/18. (End)