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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, 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*(-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

Cf. A157843, A157844.

Sequence in context: A297588 A189440 A163730 * A323742 A273550 A053017

Adjacent sequences:  A157839 A157840 A157841 * A157843 A157844 A157845

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 07 2009

STATUS

approved

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Last modified December 3 11:58 EST 2021. Contains 349462 sequences. (Running on oeis4.)