A157826 103680000n^2 - 194428800n + 91152001.

403201, 117014401, 440985601, 972316801, 1711008001, 2657059201, 3810470401, 5171241601, 6739372801, 8514864001, 10497715201, 12687926401, 15085497601, 17690428801, 20502720001, 23522371201, 26749382401, 30183753601

Offset

1,1

Comments

The identity (103680000*n^2-194428800*n+91152001)^2-(3600*n^2-6751*n+3165)*(1728000*n-1620240)^2=1 can be written as a(n)^2-A157824(n)*A157825(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*(-403201-115804798*x-91152001*x^2)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {403201, 117014401, 440985601}, 40]

Prog

(Magma) I:=[403201, 117014401, 440985601]; [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 - 194428800*n + 91152001.

Crossrefs

Cf. A157824, A157825.

Sequence in context: A234419 A096890 A234056 * A215998 A186606 A227711

Adjacent sequences: A157823 A157824 A157825 * A157827 A157828 A157829

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 07 2009

Status

approved