OFFSET
1,1
COMMENTS
The identity (169*n + 1)^2 - (169*n^2 + 2*n)*(13)^2 = 1 can be written as A158221(n)^2 - a(n)*(13)^2 = 1. - Vincenzo Librandi, Feb 02 2012
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*(13^2*t+2)).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(-171 - 167*x)/(-1+x)^3. - Harvey P. Dale, Apr 19 2011
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 02 2012
MATHEMATICA
Table[169n^2+2n, {n, 40}] (* Harvey P. Dale, Apr 19 2011 *)
LinearRecurrence[{3, -3, 1}, {171, 680, 1527}, 50] (* Vincenzo Librandi, Feb 02 2012 *)
PROG
(Magma) I:=[171, 680, 1527]; [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 02 2012
(PARI) for(n=1, 22, print1(169*n^2 + 2*n", ")); \\ Vincenzo Librandi, Feb 02 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 14 2009
STATUS
approved