A157998 169n^2 - n.

168, 674, 1518, 2700, 4220, 6078, 8274, 10808, 13680, 16890, 20438, 24324, 28548, 33110, 38010, 43248, 48824, 54738, 60990, 67580, 74508, 81774, 89378, 97320, 105600, 114218, 123174, 132468, 142100, 152070, 162378, 173024, 184008, 195330

Offset

1,1

Comments

The identity (338*n-1)^2-(169*n^2-n)*(26)^2=1 can be written as A157999(n)^2-a(n)*(26)^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 14 in the first table at p. 85, case d(t) = t*(13^2*t-1)).

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*(168+170*x)/(1-x)^3. [Colin Barker, Jan 17 2012]

Maple

A157998:=n->169*n^2 - n; seq(A157998(n), n=1..50); # Wesley Ivan Hurt, Jan 30 2014

Mathematica

LinearRecurrence[{3, -3, 1}, {168, 674, 1518}, 50]

Prog

(Magma) I:=[168, 674, 1518]; [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) = 169*n^2 - n.

Crossrefs

Cf. A157999.

Sequence in context: A266808 A234738 A234731 * A234823 A234816 A245868

Adjacent sequences: A157995 A157996 A157997 * A157999 A158000 A158001

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 11 2009

Status

approved