A157788 1482401250n^2 - 830253600n + 116250751.

768398401, 4385348551, 10967101201, 20513656351, 33025014001, 48501174151, 66942136801, 88347901951, 112718469601, 140053839751, 170354012401, 203618987551, 239848765201, 279043345351, 321202728001, 366326913151, 414415900801

Offset

1,1

Comments

The identity (1482401250*n^2-830253600*n +116250751)^2-(27225*n^2-15248*n +2135) *(8984250*n -2515920)^2=1 can be written as a(n)^2-A157786(n)*A157787(n)^2=1.

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).

Formula

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

G.f: x*(-768398401-2080153348*x-116250751*x^2)/(x-1)^3.

Mathematica

Table[1482401250n^2-830253600n+116250751, {n, 30}]

Prog

(Magma) I:=[768398401, 4385348551, 10967101201]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
(PARI) a(n) = 1482401250*n^2 - 830253600*n + 116250751.

Crossrefs

Cf. A157786, A157787.

Sequence in context: A104932 A306569 A118876 * A058420 A297867 A344729

Adjacent sequences: A157785 A157786 A157787 * A157789 A157790 A157791

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 06 2009

Status

approved