A158414 961n + 1.

962, 1923, 2884, 3845, 4806, 5767, 6728, 7689, 8650, 9611, 10572, 11533, 12494, 13455, 14416, 15377, 16338, 17299, 18260, 19221, 20182, 21143, 22104, 23065, 24026, 24987, 25948, 26909, 27870, 28831, 29792, 30753, 31714, 32675, 33636

Offset

1,1

Comments

The identity (961*n+1)^2-(961*n^2+2*n)*(31)^2=1 can be written as a(n)^2-A158413(n)*(31)^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*(31^2*t+2)).

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

Formula

G.f.: x*(962-x)/(1-x)^2.

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

Mathematica

LinearRecurrence[{2, -1}, {962, 1923}, 50]

Prog

(Magma) I:=[962, 1923]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 961*n + 1.

Crossrefs

Cf. A158413.

Sequence in context: A231761 A098207 A304315 * A031740 A031529 A347884

Adjacent sequences: A158411 A158412 A158413 * A158415 A158416 A158417

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 18 2009

Status

approved