A157266 a(n) = 1728*n - 408.

1320, 3048, 4776, 6504, 8232, 9960, 11688, 13416, 15144, 16872, 18600, 20328, 22056, 23784, 25512, 27240, 28968, 30696, 32424, 34152, 35880, 37608, 39336, 41064, 42792, 44520, 46248, 47976, 49704, 51432, 53160, 54888, 56616, 58344

Offset: 1

Author

Vincenzo Librandi, Feb 26 2009

Keywords

• nonn
• easy

Comments

The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)*(1728*n-408)^2=1 can be written as A157267(n)^2-A157265(n)*a(n)^2=1 (see also the second comment in A157267). - Vincenzo Librandi, Jan 27 2012

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Vincenzo Librandi, X^2-AY^2=1
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A157265, A157267.

Programs

Magma

I:=[1320, 3048]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 27 2012

Mathematica

LinearRecurrence[{2,-1},{1320,3048},40] (* Vincenzo Librandi, Jan 27 2012 *)
Table[1728n-408,{n,40}] (* Harvey P. Dale, Apr 18 2020 *)

PARI

for(n=1, 40, print1(1728*n - 408", ")); \\ Vincenzo Librandi, Jan 27 2012

Formula

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 27 2012

G.f.: x*(1320+408*x)/(x-1)^2. - Vincenzo Librandi, Jan 27 2012

E.g.f.: 24*((72*x - 17)*exp(x) + 17). - G. C. Greubel, Feb 04 2018