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 A157664(n)^2 - A055438(n)*a(n)^2 = 1 (see Bruno Berselli's comment at A157664). - 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 (2,-1).
FORMULA
G.f.: x*(8040 - 40*x)/(1-x)^2. - Vincenzo Librandi, Feb 04 2012
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 04 2012
E.g.f.: 40*(-1 + (1 + 200*x)*exp(x)). - G. C. Greubel, Nov 17 2018
MATHEMATICA
LinearRecurrence[{2, -1}, {8040, 16040}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
PROG
(Magma) I:=[8040, 16040]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 50, print1(8000*n + 40", ")); \\ Vincenzo Librandi, Feb 04 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