A158219 169n - 1.

168, 337, 506, 675, 844, 1013, 1182, 1351, 1520, 1689, 1858, 2027, 2196, 2365, 2534, 2703, 2872, 3041, 3210, 3379, 3548, 3717, 3886, 4055, 4224, 4393, 4562, 4731, 4900, 5069, 5238, 5407, 5576, 5745, 5914, 6083, 6252, 6421, 6590, 6759, 6928, 7097, 7266

Offset

1,1

Comments

The identity (169*n-1)^2-(1169*n^2-2*n)*(13)^2=1 can be written as a(n)^2-A158218(n)*(13)^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*(13^2*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*(168+x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {168, 337}, 50]
169*Range[50]-1 (* Harvey P. Dale, Mar 17 2018 *)

Prog

(Magma) I:=[168, 337]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 169*n - 1.

Crossrefs

Cf. A158218.

Sequence in context: A008890 A230479 A105915 * A273771 A210207 A303082

Adjacent sequences: A158216 A158217 A158218 * A158220 A158221 A158222

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved