A158133 a(n) = 144*n + 1.

145, 289, 433, 577, 721, 865, 1009, 1153, 1297, 1441, 1585, 1729, 1873, 2017, 2161, 2305, 2449, 2593, 2737, 2881, 3025, 3169, 3313, 3457, 3601, 3745, 3889, 4033, 4177, 4321, 4465, 4609, 4753, 4897, 5041, 5185, 5329, 5473, 5617, 5761, 5905, 6049, 6193

Offset

1,1

Comments

The identity (144*n+1)^2-(144*n^2+2*n)*(12)^2=1 can be written as a(n)^2-A158132(n)*(12)^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*(12^2*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*(145-x)/(1-x)^2.

Mathematica

LinearRecurrence[{2, -1}, {145, 289}, 50]

Prog

(Magma) I:=[145, 289]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n) = 144n + 1.

Crossrefs

Cf. A158132.

Sequence in context: A176699 A177223 A318530 * A094613 A207058 A116208

Adjacent sequences: A158130 A158131 A158132 * A158134 A158135 A158136

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 13 2009

Status

approved