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A158598 a(n) = 40*n^2 - 1. 2

%I

%S 39,159,359,639,999,1439,1959,2559,3239,3999,4839,5759,6759,7839,8999,

%T 10239,11559,12959,14439,15999,17639,19359,21159,23039,24999,27039,

%U 29159,31359,33639,35999,38439,40959,43559,46239,48999,51839,54759

%N a(n) = 40*n^2 - 1.

%C The identity (40*n^2 - 1)^2 - (400*n^2 - 20)*(2*n)^2 = 1 can be written as a(n)^2 - A158597(n)*A005843(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A158598/b158598.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0"> X^2-AY^2=1</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: x*(-39 - 42*x + x^2)/(x-1)^3.

%F a(n)= 3*a(n-1) - 3*a(n-2) + a(n-3).

%t LinearRecurrence[{3, -3, 1}, {39, 159, 359}, 50] (* _Vincenzo Librandi_, Feb 16 2012 *)

%o (MAGMA) I:=[39, 159, 359]; [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_, Feb 16 2012

%o (PARI) for(n=1, 40, print1(40*n^2 - 1", ")); \\ _Vincenzo Librandi_, Feb 16 2012

%Y Cf. A005843, A158597.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 22 2009

%E Comment rewritten, formula replaced by _R. J. Mathar_, Oct 28 2009

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Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)