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A157442 a(n) = 14641*n^2 - 24684*n + 10405.

%I A157442 #25 Sep 08 2022 08:45:42
%S A157442 362,19601,68122,145925,253010,389377,555026,749957,974170,1227665,
%T A157442 1510442,1822501,2163842,2534465,2934370,3363557,3822026,4309777,
%U A157442 4826810,5373125,5948722,6553601,7187762,7851205,8543930,9265937
%N A157442 a(n) = 14641*n^2 - 24684*n + 10405.
%C A157442 The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as a(n)^2 - A157440(n)*A157441(n)^2 = 1. - _Vincenzo Librandi_, Jan 29 2012
%H A157442 Harvey P. Dale, <a href="/A157442/b157442.txt">Table of n, a(n) for n = 1..1000</a>
%H A157442 Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&amp;tstart=0">X^2-AY^2=1</a>
%H A157442 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A157442 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=362, a(2)=19601, a(3)=68122. - _Harvey P. Dale_, Oct 22 2011
%F A157442 G.f.: x*(-10405*x^2 - 18515*x - 362)/(x-1)^3. - _Harvey P. Dale_, Oct 22 2011
%F A157442 a(n) = A017485(11*n-10)^2 + 1. - _Bruno Berselli_, Jan 29 2012
%t A157442 Table[14641n^2-24684n+10405,{n,30}] (* or *) LinearRecurrence[{3,-3,1},{362,19601,68122},30]
%o A157442 (Magma) I:=[362, 19601, 68122]; [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 29 2012
%o A157442 (PARI) for(n=1, 40, print1(14641*n^2 - 24684*n + 10405", ")); \\ _Vincenzo Librandi_, Jan 29 2012
%Y A157442 Cf. A017485, A157440, A157441.
%K A157442 nonn,easy
%O A157442 1,1
%A A157442 _Vincenzo Librandi_, Mar 01 2009