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 A157514 a(n) = 25*n^2 - n. 3

%I

%S 24,98,222,396,620,894,1218,1592,2016,2490,3014,3588,4212,4886,5610,

%T 6384,7208,8082,9006,9980,11004,12078,13202,14376,15600,16874,18198,

%U 19572,20996,22470,23994,25568,27192,28866,30590,32364,34188,36062

%N a(n) = 25*n^2 - n.

%C The identity (5000*n^2 - 200*n + 1)^2 - (25*n^2 - n)*(1000*n - 20)^2 = 1 can be written as A157516(n)^2 - a(n)*A157515(n)^2 = 1. This is the case s=5 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 26 2012

%H Vincenzo Librandi, <a href="/A157514/b157514.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_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 26 2012

%F G.f.: x*(-24 - 26*x)/(x-1)^3. - _Vincenzo Librandi_, Jan 26 2012

%t LinearRecurrence[{3,-3,1},{24,98,222},50] (* _Vincenzo Librandi_, Jan 26 2012 *)

%o (MAGMA) I:=[24, 98, 222]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Jan 26 2012

%o (PARI) for(n=1, 22, print1(25*n^2 - n", ")); \\ _Vincenzo Librandi_, Jan 26 2012

%Y Cf. A157515, A157516.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 02 2009

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Last modified December 3 18:19 EST 2021. Contains 349467 sequences. (Running on oeis4.)