A158067 a(n) = 64*n^2 - 2*n.

62, 252, 570, 1016, 1590, 2292, 3122, 4080, 5166, 6380, 7722, 9192, 10790, 12516, 14370, 16352, 18462, 20700, 23066, 25560, 28182, 30932, 33810, 36816, 39950, 43212, 46602, 50120, 53766, 57540, 61442, 65472, 69630, 73916, 78330, 82872

Offset: 1

Author

Vincenzo Librandi, Mar 12 2009

Keywords

• nonn
• easy

Comments

The identity (64*n - 1)^2 - (64*n^2 - 2*n)*8^2 = 1 can be written as (A152691(n+1) - 1)^2 - a(n)*8^2 = 1. - Vincenzo Librandi, Feb 11 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(8^2*t-2)).
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A152691.

Programs

Magma

[64*n^2 - 2*n: n in [1..50]]

Mathematica

LinearRecurrence[{3, -3, 1}, {62, 252, 570}, 50] (* Vincenzo Librandi, Feb 11 2012 *)
Table[64n^2-2n,{n,40}] (* Harvey P. Dale, Nov 27 2024 *)

PARI

for(n=1, 50, print1(64*n^2 - 2*n ", ")); \\ Vincenzo Librandi, Feb 11 2012

Formula

G.f.: x*(-62 - 66*x)/(x-1)^3. - Vincenzo Librandi, Feb 11 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 11 2012