A158225 196n - 1.

195, 391, 587, 783, 979, 1175, 1371, 1567, 1763, 1959, 2155, 2351, 2547, 2743, 2939, 3135, 3331, 3527, 3723, 3919, 4115, 4311, 4507, 4703, 4899, 5095, 5291, 5487, 5683, 5879, 6075, 6271, 6467, 6663, 6859, 7055, 7251, 7447, 7643, 7839, 8035, 8231, 8427

Offset

1,1

Comments

The identity (196*n-1)^2-(196*n^2-2*n)*(14)^2=1 can be written as a(n)^2-A158224(n)*(14)^2=1.

Links

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

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(14^2*t-2)).

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

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

G.f.: x*(195+x)/(1-x)^2.

Mathematica

196Range[60]-1  (* Harvey P. Dale, Mar 23 2011 *)
LinearRecurrence[{2, -1}, {195, 391}, 50]

Prog

(Magma) I:=[195, 391]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 196*n - 1.

Crossrefs

Cf. A158224.

Sequence in context: A080394 A323975 A055970 * A080913 A343339 A157239

Adjacent sequences: A158222 A158223 A158224 * A158226 A158227 A158228

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved