A157432 64n + 584.

648, 712, 776, 840, 904, 968, 1032, 1096, 1160, 1224, 1288, 1352, 1416, 1480, 1544, 1608, 1672, 1736, 1800, 1864, 1928, 1992, 2056, 2120, 2184, 2248, 2312, 2376, 2440, 2504, 2568, 2632, 2696, 2760, 2824, 2888, 2952, 3016, 3080, 3144, 3208, 3272, 3336

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-A157431(n)*a(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 (2,-1).

Formula

a(n) = 2*a(n-1)-a(n-2).

G.f.: x*(648-584x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {648, 712}, 50]
64*Range[50]+584 (* Harvey P. Dale, Sep 09 2012 *)

Prog

(Magma) I:=[648, 712]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 64*n + 584.

Crossrefs

Cf. A157431, A157433.

Sequence in context: A334896 A271639 A034281 * A272780 A171606 A006914

Adjacent sequences: A157429 A157430 A157431 * A157433 A157434 A157435

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 01 2009

Status

approved