A157325 a(n) = 1728*n + 24.

1752, 3480, 5208, 6936, 8664, 10392, 12120, 13848, 15576, 17304, 19032, 20760, 22488, 24216, 25944, 27672, 29400, 31128, 32856, 34584, 36312, 38040, 39768, 41496, 43224, 44952, 46680, 48408, 50136, 51864, 53592, 55320, 57048, 58776

Offset: 1

Author

Vincenzo Librandi, Feb 27 2009

Keywords

• nonn
• easy

Comments

The identity (10368*n^2 + 288*n + 1)^2 - (36*n^2 + n)*(1728*n + 24)^2 = 1 can be written as A157326(n)^2 - A157324(n)*a(n)^2 = 1 (see also second part of the comment at A157324). - Vincenzo Librandi, Jan 26 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. A157324, A157326.

Programs

Magma

I:=[1752, 3480]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jan 26 2012

Mathematica

LinearRecurrence[{2,-1},{1752,3480},50] (* Vincenzo Librandi, Jan 26 2012 *)
1728*Range[40]+24 (* Harvey P. Dale, Feb 28 2016 *)

PARI

for(n=1, 22, print1(1728*n + 24", ")); \\ Vincenzo Librandi, Jan 26 2012

Formula

G.f.: x*(1752 - 24*x)/(1-x)^2. - Vincenzo Librandi, Jan 26 2012

a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 26 2012