A158420 1024n^2 - 2n.

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

1,1

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).

Formula

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

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

Mathematica

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

Prog

(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]];
(PARI) a(n) = 1024*n^2 - 2*n.

Crossrefs

Cf. A158421.

Sequence in context: A261676 A165097 A165101 * A196739 A196291 A145589

Adjacent sequences: A158417 A158418 A158419 * A158421 A158422 A158423

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved