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A157840 103680000n^2 - 174211200n + 73180801. 3
2649601, 139478401, 483667201, 1035216001, 1794124801, 2760393601, 3934022401, 5315011201, 6903360001, 8699068801, 10702137601, 12912566401, 15330355201, 17955504001, 20788012801, 23827881601, 27075110401, 30529699201 (list; graph; refs; listen; history; text; internal format)
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, X^2-AY^2=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
Sequence in context: A196496 A105380 A250911 * A063413 A210388 A251044
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 07 2009
STATUS
approved

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Last modified July 13 17:55 EDT 2024. Contains 374285 sequences. (Running on oeis4.)