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A157661
a(n) = 80000*n^2 - 800*n + 1.
3
79201, 318401, 717601, 1276801, 1996001, 2875201, 3914401, 5113601, 6472801, 7992001, 9671201, 11510401, 13509601, 15668801, 17988001, 20467201, 23106401, 25905601, 28864801, 31984001, 35263201, 38702401, 42301601, 46060801
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 a(n)^2 - A157659(n)* A157660(n)^2 = 1. This is the case s=10 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1. - Vincenzo Librandi, Jan 28 2012
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 28 2012
G.f.: x*(-79201 - 80798*x - x^2)/(x-1)^3. - Vincenzo Librandi, Jan 28 2012
E.g.f.: (1 + 79200*x + 80000*x^2)*exp(x) - 1. G. C. Greubel, Nov 17 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {79201, 318401, 717601}, 40] (* Vincenzo Librandi, Jan 28 2012 *)
PROG
(Magma) I:=[79201, 318401, 717601]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 28 2012
(PARI) for(n=1, 40, print1(80000*n^2 - 800*n + 1, ", ")); \\ Vincenzo Librandi, Jan 28 2012
(Sage) [80000*n^2-800*n+1 for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 80000*n^2-800*n+1); # G. C. Greubel, Nov 17 2018
CROSSREFS
Sequence in context: A264950 A204570 A183640 * A159713 A251208 A103873
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 04 2009
STATUS
approved