A157326 a(n) = 10368*n^2 + 288*n + 1.

10657, 42049, 94177, 167041, 260641, 374977, 510049, 665857, 842401, 1039681, 1257697, 1496449, 1755937, 2036161, 2337121, 2658817, 3001249, 3364417, 3748321, 4152961, 4578337, 5024449, 5491297, 5978881, 6487201, 7016257

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 a(n)^2 - A157324(n)*A157325(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 (3,-3,1).

Crossrefs

Cf. A157324, A157325.

Programs

Magma

I:=[10657, 42049, 94177]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 26 2012

Mathematica

LinearRecurrence[{3,-3,1},{10657,42049,94177},50] (* Vincenzo Librandi, Jan 26 2012 *)

PARI

for(n=1, 22, print1(10368*n^2 + 288*n + 1", ")); \\ Vincenzo Librandi, Jan 26 2012

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012

G.f.: x*(-x^2 - 10078*x - 10657)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012

a(n) = 2*A017533(6n)^2 - 1. - Bruno Berselli, Jan 29 2012