A158003 a(n) = 196*n^2 - n.

195, 782, 1761, 3132, 4895, 7050, 9597, 12536, 15867, 19590, 23705, 28212, 33111, 38402, 44085, 50160, 56627, 63486, 70737, 78380, 86415, 94842, 103661, 112872, 122475, 132470, 142857, 153636, 164807, 176370, 188325, 200672, 213411, 226542

Offset

1,1

Comments

The identity (392*n - 1)^2 - (196*n^2 - n)*28^2 = 1 can be written as A158004(n)^2 - a(n)*28^2 = 1. - Vincenzo Librandi, Feb 10 2012

Links

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

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*(14^2*t-1)).

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

Formula

G.f.: x*(-195 - 197*x)/(x-1)^3. - Vincenzo Librandi, Feb 10 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 10 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {195, 782, 1761}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

Prog

(Magma) I:=[195, 782, 1761]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012
(PARI) for(n=1, 50, print1(196*n^2 - n", ")); \\ Vincenzo Librandi, Feb 10 2012

Crossrefs

Cf. A158004.

Sequence in context: A080913 A343339 A157239 * A225713 A172354 A295130

Adjacent sequences: A158000 A158001 A158002 * A158004 A158005 A158006

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 11 2009

Status

approved