OFFSET
1,1
COMMENTS
The identity (80000*n^2 - 800*n + 1)^2 - (100*n^2 - n)*(8000*n - 40)^2 = 1 can be written as A157661(n)^2 - A157659(n)*a(n)^2 = 1 (see also the second part of the comment at A157661). - Vincenzo Librandi, Jan 28 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 (2,-1).
FORMULA
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jan 28 2012
G.f.: x*(40*x+7960)/(x-1)^2. - Vincenzo Librandi, Jan 28 2012
E.g.f.: 40*(1 - (1 - 200*x)*exp(x)). G. C. Greubel, Nov 17 2018
MATHEMATICA
LinearRecurrence[{2, -1}, {7960, 15960}, 40] (* Vincenzo Librandi, Jan 28 2012 *)
PROG
(Magma) I:=[7960, 15960]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(8000*n-40", ")); \\ Vincenzo Librandi, Jan 28 2012
(Sage) [40*(200*n - 1) for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 40*(200*n - 1)); # G. C. Greubel, Nov 17 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 04 2009
STATUS
approved