A157844 103680000n^2 - 161251200n + 62697601.

5126401, 154915201, 512064001, 1076572801, 1848441601, 2827670401, 4014259201, 5408208001, 7009516801, 8818185601, 10834214401, 13057603201, 15488352001, 18126460801, 20971929601, 24024758401, 27284947201, 30752496001

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 a(n)^2-A157842(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*(-5126401-139535998*x-62697601*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {5126401, 154915201, 512064001}, 40]

Prog

(Magma) I:=[5126401, 154915201, 512064001]; [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 - 161251200*n + 62697601.

Crossrefs

Cf. A157842, A157843.

Sequence in context: A234785 A206136 A186624 * A263039 A241607 A140658

Adjacent sequences: A157841 A157842 A157843 * A157845 A157846 A157847

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved