A157628 80000n^2 - 120800n + 45601.

4801, 124001, 403201, 842401, 1441601, 2200801, 3120001, 4199201, 5438401, 6837601, 8396801, 10116001, 11995201, 14034401, 16233601, 18592801, 21112001, 23791201, 26630401, 29629601, 32788801, 36108001, 39587201, 43226401

Offset

1,1

Comments

The identity (80000*n^2-120800*n+45601)^2-(100*n^2-151*n +57)*(8000*n-6040)^2=1 can be written as a(n)^2-A157626(n)*A157627(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*(-4801-109598*x-45601*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {4801, 124001, 403201}, 40]
Rest[CoefficientList[Series[x (-4801-109598x-45601x^2)/(x-1)^3, {x, 0, 30}], x]] (* Harvey P. Dale, Apr 30 2022 *)

Prog

(Magma) I:=[4801, 124001, 403201]; [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)=80000*n^2-120800*n+45601 \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A157626, A157627.

Sequence in context: A254791 A096790 A157516 * A214146 A085322 A336536

Adjacent sequences: A157625 A157626 A157627 * A157629 A157630 A157631

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved