A157840 103680000n^2 - 174211200n + 73180801.

2649601, 139478401, 483667201, 1035216001, 1794124801, 2760393601, 3934022401, 5315011201, 6903360001, 8699068801, 10702137601, 12912566401, 15330355201, 17955504001, 20788012801, 23827881601, 27075110401, 30529699201

Offset

1,1

Comments

The identity (103680000*n^2-174211200*n+73180801)^2-(3600*n^2-6049*n+2541)*(1728000*n-1451760)^2=1 can be written as a(n)^2-A157838(n)*A157839(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*(-2649601-131529598*x-73180801*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {2649601, 139478401, 483667201}, 40]
Table[103680000n^2-174211200n+73180801, {n, 20}] (* Harvey P. Dale, Feb 19 2024 *)

Prog

(Magma) I:=[2649601, 139478401, 483667201]; [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) = 103680000*n^2 - 174211200*n + 73180801.

Crossrefs

Cf. A157838, A157839.

Sequence in context: A196496 A105380 A250911 * A063413 A210388 A251044

Adjacent sequences: A157837 A157838 A157839 * A157841 A157842 A157843

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved