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A158734 a(n) = 70*n^2 + 1. 2

%I

%S 1,71,281,631,1121,1751,2521,3431,4481,5671,7001,8471,10081,11831,

%T 13721,15751,17921,20231,22681,25271,28001,30871,33881,37031,40321,

%U 43751,47321,51031,54881,58871,63001,67271,71681,76231,80921,85751,90721

%N a(n) = 70*n^2 + 1.

%C The identity (70*n^2 + 1)^2 - (1225*n^2 + 35)*(2*n)^2 = 1 can be written as a(n)^2 - A158733(n)*A005843(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A158734/b158734.txt">Table of n, a(n) for n = 0..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.: -(1 + 68*x + 71*x^2)/(x-1)^3.

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

%t LinearRecurrence[{3, -3, 1}, {1, 71, 281}, 50] (* _Vincenzo Librandi_, Feb 20 2012 *)

%o (MAGMA) I:=[1, 71, 281]; [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 20 2012

%o (PARI) for(n=0, 40, print1(70*n^2 + 1", ")); \\ _Vincenzo Librandi_, Feb 20 2012

%Y Cf. A005843, A158733.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Mar 25 2009

%E Comment rewritten, a(0) added and formula replaced by _R. J. Mathar_, Oct 22 2009

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Last modified May 7 12:05 EDT 2021. Contains 343650 sequences. (Running on oeis4.)