A157610 29282n^2 - 484n + 1.

28799, 116161, 262087, 466577, 729631, 1051249, 1431431, 1870177, 2367487, 2923361, 3537799, 4210801, 4942367, 5732497, 6581191, 7488449, 8454271, 9478657, 10561607, 11703121, 12903199, 14161841, 15479047, 16854817, 18289151

Offset

1,1

Comments

The identity (29282*n^2-484*n+1)^2-(121*n^2-2*n)*(2662*n-22)^2=1 can be written as (a(n))^2-(A157040(n))* (A157609(n)) ^2=1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Wolfram MathWorld, Pell Equation

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*(-28799-29764*x-x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {28799, 116161, 262087}, 40]

Prog

(Magma) I:=[28799, 116161, 262087]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n) = 29282*n^2-484*n+1.

Crossrefs

Cf. A157040, A157609.

Sequence in context: A259047 A237321 A249957 * A250011 A237727 A252319

Adjacent sequences: A157607 A157608 A157609 * A157611 A157612 A157613

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved