A158228 a(n) = 225n^2 + 2n.

227, 904, 2031, 3608, 5635, 8112, 11039, 14416, 18243, 22520, 27247, 32424, 38051, 44128, 50655, 57632, 65059, 72936, 81263, 90040, 99267, 108944, 119071, 129648, 140675, 152152, 164079, 176456, 189283, 202560, 216287, 230464, 245091, 260168

Offset

1,1

Comments

The identity (225*n+1)^2-(225*n^2+2*n)*(15)^2=1 can be written as A158229(n)^2-a(n)*(15)^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*(15^2*t+2)).

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

Formula

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

G.f.: x*(-223*x-227)/(x-1)^3.

Mathematica

LinearRecurrence[{3, -3, 1}, {227, 904, 2031}, 50]

Prog

(Magma) I:=[227, 904, 2031]; [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) = 225*n^2 + 2*n.

Crossrefs

Cf. A158229.

Sequence in context: A142219 A176012 A031693 * A349985 A209843 A115998

Adjacent sequences: A158225 A158226 A158227 * A158229 A158230 A158231

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 14 2009

Status

approved