A157434 a(n) = 4*n^2 + 79*n + 390.

473, 564, 663, 770, 885, 1008, 1139, 1278, 1425, 1580, 1743, 1914, 2093, 2280, 2475, 2678, 2889, 3108, 3335, 3570, 3813, 4064, 4323, 4590, 4865, 5148, 5439, 5738, 6045, 6360, 6683, 7014, 7353, 7700, 8055, 8418, 8789, 9168, 9555, 9950, 10353, 10764

Offset

1,1

Comments

The identity (128*n^2 + 2528*n + 12481)^2 - (4*n^2 + 79*n + 390)*(64*n + 632)^2 = 1 can be written as A157436(n)^2 - a(n)*A157435(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*(-390*x^2 + 855*x - 473)/(x-1)^3. [corrected by Georg Fischer, May 11 2019]

Mathematica

LinearRecurrence[{3, -3, 1}, {473, 564, 663}, 50]

Prog

(Magma) I:=[473, 564, 663]; [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 + 79*n + 390

Crossrefs

Cf. A157435, A157436.

Sequence in context: A180838 A006180 A074654 * A084629 A075286 A235897

Adjacent sequences: A157431 A157432 A157433 * A157435 A157436 A157437

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 01 2009

Status

approved