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A157613 a(n) = 2662*n + 22. 3

%I #26 Nov 14 2023 21:35:47

%S 2684,5346,8008,10670,13332,15994,18656,21318,23980,26642,29304,31966,

%T 34628,37290,39952,42614,45276,47938,50600,53262,55924,58586,61248,

%U 63910,66572,69234,71896,74558,77220,79882,82544,85206,87868,90530

%N a(n) = 2662*n + 22.

%C The identity (29282*n^2 + 484*n + 1)^2 - (121*n^2 + 2*n)*(2662*n + 22)^2 = 1 can be written as A157614(n)^2 - A181679(n)*a(n)^2 = 1 (see also _Bruno Berselli_'s comment in A181679). - _Vincenzo Librandi_, Feb 21 2012

%H Vincenzo Librandi, <a href="/A157613/b157613.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5771301&amp;tstart=0">X^2-AY^2=1</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F From _Vincenzo Librandi_, Feb 21 2012: (Start)

%F G.f.: x*(2684 - 22*x)/(1-x)^2;

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

%t LinearRecurrence[{2, -1}, {2684, 5346}, 50] (* _Vincenzo Librandi_, Feb 21 2012 *)

%t 2662 Range[40] + 22 (* _Wesley Ivan Hurt_, Nov 14 2023 *)

%o (Magma) I:=[2684, 5346]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 21 2012

%o (PARI) for(n=1, 50, print1(2662*n + 22", ")); \\ _Vincenzo Librandi_, Feb 21 2012

%Y Cf. A157614, A181679.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 03 2009

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Last modified March 28 08:19 EDT 2024. Contains 371236 sequences. (Running on oeis4.)