A173089 a(n) = 25*n^2 + n.

26, 102, 228, 404, 630, 906, 1232, 1608, 2034, 2510, 3036, 3612, 4238, 4914, 5640, 6416, 7242, 8118, 9044, 10020, 11046, 12122, 13248, 14424, 15650, 16926, 18252, 19628, 21054, 22530, 24056, 25632, 27258, 28934, 30660, 32436, 34262, 36138, 38064, 40040, 42066, 44142, 46268, 48444, 50670, 52946, 55272, 57648

Offset

1,1

Comments

The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as A157511(n)^2 - a(n)*A157510(n)^2 = 1. This is the case s=5 of the identity (8*n^2*s^4 + 8*n*s^2 + 1)^2 -(n^2*s^2 + n)*(8*n*s^3 + 4*s)^2 = 1. - Vincenzo Librandi, Feb 04 2012

Links

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

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

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

Formula

G.f.: x*(-26 - 24*x)/(x-1)^3. - Vincenzo Librandi, Feb 04 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 04 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {26, 102, 228}, 50] (* Vincenzo Librandi, Feb 04 2012 *)

Prog

(Magma) [ 25*n^2+n: n in [1..50] ];
(PARI) for(n=1, 40, print1(25*n^2 + n", ")); \\ Vincenzo Librandi, Feb 04 2012

Crossrefs

Cf. A157510, A157511.

Sequence in context: A136293 A065013 A031434 * A333055 A244633 A042320

Adjacent sequences: A173086 A173087 A173088 * A173090 A173091 A173092

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 22 2010

Status

approved