A157855 103680000n^2 - 46108800n + 5126401.

62697601, 327628801, 799920001, 1479571201, 2366582401, 3460953601, 4762684801, 6271776001, 7988227201, 9912038401, 12043209601, 14381740801, 16927632001, 19680883201, 22641494401, 25809465601, 29184796801, 32767488001

Offset

1,1

Comments

The identity (103680000*n^2-46108800*n+5126401)^2-(3600*n^2-1601*n +178)*(1728000*n-384240)^2=1 can be written as a(n)^2-A157853(n)*A157854(n)^2=1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Mathematica

LinearRecurrence[{3, -3, 1}, {62697601, 327628801, 799920001}, 40]

Prog

(Magma) I:=[62697601, 327628801, 799920001]; [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 - 46108800*n + 5126401.

Crossrefs

Cf. A157853, A157854.

Sequence in context: A205658 A206187 A205369 * A017539 A227150 A186140

Adjacent sequences: A157852 A157853 A157854 * A157856 A157857 A157858

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 08 2009

Status

approved