A158420 a(n) = 1024*n^2 - 2*n.

1022, 4092, 9210, 16376, 25590, 36852, 50162, 65520, 82926, 102380, 123882, 147432, 173030, 200676, 230370, 262112, 295902, 331740, 369626, 409560, 451542, 495572, 541650, 589776, 639950, 692172, 746442, 802760, 861126, 921540, 984002

Offset: 1

Author

Vincenzo Librandi, Mar 18 2009

Keywords

• nonn
• easy

Comments

The identity (1024*n-1)^2-(1024*n^2-2*n)*(32)^2=1 can be written as A158421(n)^2-a(n)*(32)^2=1.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Vincenzo Librandi, X^2-AY^2=1
• 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*(32^2*t-2)).
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A158421.

Programs

Magma

I:=[1022, 4092, 9210]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

Mathematica

LinearRecurrence[{3,-3,1},{1022,4092,9210},50]

PARI

a(n) = 1024*n^2 - 2*n

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(-1022-1026*x)/(x-1)^3.