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A157842 a(n) = 3600*n^2 - 5599*n + 2177. 3
178, 5379, 17780, 37381, 64182, 98183, 139384, 187785, 243386, 306187, 376188, 453389, 537790, 629391, 728192, 834193, 947394, 1067795, 1195396, 1330197, 1472198, 1621399, 1777800, 1941401, 2112202, 2290203, 2475404, 2667805 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (103680000*n^2-161251200*n+62697601)^2-(3600*n^2-5599*n+2177)*(1728000*n-1343760)^2=1 can be written as A157844(n)^2-a(n)*A157843(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*(-178-4845*x-2177*x^2)/(x-1)^3.
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {178, 5379, 17780}, 40]
PROG
(Magma) I:=[178, 5379, 17780]; [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) = 3600*n^2 - 5599*n + 2177.
CROSSREFS
Sequence in context: A297588 A189440 A163730 * A323742 A273550 A053017
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 07 2009
STATUS
approved

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Last modified July 16 08:10 EDT 2024. Contains 374345 sequences. (Running on oeis4.)