A157040 121n^2 - 2n.

119, 480, 1083, 1928, 3015, 4344, 5915, 7728, 9783, 12080, 14619, 17400, 20423, 23688, 27195, 30944, 34935, 39168, 43643, 48360, 53319, 58520, 63963, 69648, 75575, 81744, 88155, 94808, 101703, 108840, 116219, 123840, 131703, 139808

Offset

1,1

Comments

The identity (29282*n^2-484*n+1)^2-(121*n^2-2*n)*(2662*n-22)^2=1 can be written as A157610(n)^2-a(n)*A157609(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*(-119-123*x)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {119, 480, 1083}, 40]

Prog

(Magma) I:=[119, 480, 1083]; [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) = 121*n^2-2*n.

Crossrefs

Cf. A157610, A157609.

Sequence in context: A063348 A243581 A103852 * A256907 A049226 A106572

Adjacent sequences: A157037 A157038 A157039 * A157041 A157042 A157043

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 03 2009

Status

approved