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A157788 1482401250n^2 - 830253600n + 116250751. 3
768398401, 4385348551, 10967101201, 20513656351, 33025014001, 48501174151, 66942136801, 88347901951, 112718469601, 140053839751, 170354012401, 203618987551, 239848765201, 279043345351, 321202728001, 366326913151, 414415900801 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 24 15:40 EDT 2021. Contains 347643 sequences. (Running on oeis4.)