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A157264 a(n) = 10368*n^2 - 15840*n + 6049. 3

%I #19 Sep 08 2022 08:45:41

%S 577,15841,51841,108577,186049,284257,403201,542881,703297,884449,

%T 1086337,1308961,1552321,1816417,2101249,2406817,2733121,3080161,

%U 3447937,3836449,4245697,4675681,5126401,5597857,6090049,6602977

%N a(n) = 10368*n^2 - 15840*n + 6049.

%C The identity (10368*n^2-15840*n+6049)^2-(36*n^2-55*n+21)*(1728*n-1320)^2=1 can be written as a(n)^2-A157262(n)*A157263(n)^2=1. - _Vincenzo Librandi_, Jan 27 2012

%H Vincenzo Librandi, <a href="/A157264/b157264.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 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 27 2012

%F G.f.: x*(-577-14110*x-6049*x^2)/(x-1)^3. - _Vincenzo Librandi_, Jan 27 2012

%F E.g.f.: (10368*x^2 - 5472*x + 6049)*exp(x) - 6049. - _G. C. Greubel_, Feb 04 2018

%t LinearRecurrence[{3,-3,1},{577,15841,51841},40] (* _Vincenzo Librandi_, Jan 27 2012 *)

%o (Magma) I:=[577, 15841, 51841]; [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 27 2012

%o (PARI) for(n=1, 40, print1(10368*n^2 - 15840*n + 6049", ")); \\ _Vincenzo Librandi_, Jan 27 2012

%Y Cf. A157262, A157263.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 26 2009

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Last modified April 20 00:26 EDT 2024. Contains 371798 sequences. (Running on oeis4.)