A158254 a(n) = 289n^2 + 2n.

291, 1160, 2607, 4632, 7235, 10416, 14175, 18512, 23427, 28920, 34991, 41640, 48867, 56672, 65055, 74016, 83555, 93672, 104367, 115640, 127491, 139920, 152927, 166512, 180675, 195416, 210735, 226632, 243107, 260160, 277791, 296000, 314787

Offset

1,1

Comments

The identity (289*n+1)^2-(289*n^2+2*n)*(17)^2=1 can be written as A158255(n)^2-a(n)*(17)^2=1.

Links

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

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*(17^2*t+2)).

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(291+287*x)/(1-x)^3. Also a(n) = (A158255(n)+1)*n. - Bruno Berselli, Mar 21 2011

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

Mathematica

LinearRecurrence[{3, -3, 1}, {291, 1160, 2607}, 50]
Table[289n^2+2n, {n, 40}] (* Harvey P. Dale, Jun 05 2013 *)

Prog

(Magma) I:=[291, 1160, 2607]; [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) = 289*n^2 + 2*n.

Crossrefs

Cf. A158255.

Sequence in context: A090890 A123913 A031695 * A088892 A098248 A185999

Adjacent sequences: A158251 A158252 A158253 * A158255 A158256 A158257

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 15 2009

Status

approved