A157264 a(n) = 10368*n^2 - 15840*n + 6049.

577, 15841, 51841, 108577, 186049, 284257, 403201, 542881, 703297, 884449, 1086337, 1308961, 1552321, 1816417, 2101249, 2406817, 2733121, 3080161, 3447937, 3836449, 4245697, 4675681, 5126401, 5597857, 6090049, 6602977

Offset: 1

Author

Vincenzo Librandi, Feb 26 2009

Keywords

• nonn
• easy

Comments

The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as a(n)^2-A157262(n)*A157263(n)^2=1. - 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 (3,-3,1).

Crossrefs

Cf. A157262, A157263.

Programs

Magma

I:=[577, 15841, 51841]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 27 2012

Mathematica

LinearRecurrence[{3,-3,1},{577,15841,51841},40] (* Vincenzo Librandi, Jan 27 2012 *)
Table[10368n^2-15840n+6049,{n,30}] (* Harvey P. Dale, Nov 18 2024 *)

PARI

for(n=1, 40, print1(10368*n^2 - 15840*n + 6049", ")); \\ Vincenzo Librandi, Jan 27 2012

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 27 2012

G.f.: x*(-577-14110*x-6049*x^2)/(x-1)^3. - Vincenzo Librandi, Jan 27 2012

E.g.f.: (10368*x^2 - 5472*x + 6049)*exp(x) - 6049. - G. C. Greubel, Feb 04 2018