A157822 1482401250n^2+108900n+1.

1482510151, 5929822801, 13341937951, 23718855601, 37060575751, 53367098401, 72638423551, 94874551201, 120075481351, 148241214001, 179371749151, 213467086801, 250527226951, 290552169601, 333541914751, 379496462401, 428415812551

Offset

1,1

Comments

The identity (1482401250*n^2+108900*n+1)^2-(27225*n^2+2*n)*(8984250*n+330)^2=1 can be written as a(n)^2-A157820(n)*A157821(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*(-x^2-1482292348*x-1482510151)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {1482510151, 5929822801, 13341937951}, 30]

Prog

(Magma) I:=[1482510151, 5929822801, 13341937951]; [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+108900*n+1.

Crossrefs

Cf. A157820, A157821

Sequence in context: A320873 A166113 A157816 * A034616 A084551 A206045

Adjacent sequences: A157819 A157820 A157821 * A157823 A157824 A157825

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved