A157431 a(n) = 4*n^2 + 73*n + 333.

410, 495, 588, 689, 798, 915, 1040, 1173, 1314, 1463, 1620, 1785, 1958, 2139, 2328, 2525, 2730, 2943, 3164, 3393, 3630, 3875, 4128, 4389, 4658, 4935, 5220, 5513, 5814, 6123, 6440, 6765, 7098, 7439, 7788, 8145, 8510, 8883, 9264, 9653, 10050, 10455

Offset

1,1

Comments

The identity (128*n^2+2336*n+10657)^2-(4*n^2+73*n+333)*(64*n+584)^2=1 can be written as A157433(n)^2-a(n)*A157432(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.: -(264*x^2-589*x+333)/(x-1)^3. [corrected by Georg Fischer, May 12 2019]

Mathematica

LinearRecurrence[{3, -3, 1}, {410, 495, 588}, 50]

Prog

(Magma) I:=[410, 495, 588]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 4*n^2 + 73*n + 333.

Crossrefs

Cf. A157432, A157433.

Sequence in context: A061333 A262636 A238753 * A179129 A176598 A146075

Adjacent sequences: A157428 A157429 A157430 * A157432 A157433 A157434

Keyword

nonn,easy,changed

Author

Vincenzo Librandi, Mar 01 2009

Status

approved