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%I #26 Oct 05 2024 21:27:08
%S 163,325,487,649,811,973,1135,1297,1459,1621,1783,1945,2107,2269,2431,
%T 2593,2755,2917,3079,3241,3403,3565,3727,3889,4051,4213,4375,4537,
%U 4699,4861,5023,5185,5347,5509,5671,5833,5995,6157,6319,6481,6643,6805,6967
%N a(n) = 162*n + 1.
%C The identity (162*n + 1)^2 - (81*n^2 + n)*18^2 = 1 can be written as a(n)^2 - (A017162(n) + n)*18^2 = 1. - _Vincenzo Librandi_, Feb 10 2012
%H Vincenzo Librandi, <a href="/A157952/b157952.txt">Table of n, a(n) for n = 1..10000</a>
%H E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(9^2*t+1)).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F a(n) = 2*a(n-1) - a(n-2), a(0)=163, a(1)=325. - _Harvey P. Dale_, Aug 10 2011
%F G.f.: x*(163-x)/(1-x)^2. - _Vincenzo Librandi_, Feb 10 2012
%t 162Range[50]+1 (* or *) LinearRecurrence[{2,-1},{163,325},50](* _Harvey P. Dale_, Aug 10 2011 *)
%o (Magma) I:=[163, 325]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 10 2012
%o (PARI) for(n=1, 50, print1(162*n+1", ")); \\ _Vincenzo Librandi_, Feb 10 2012
%Y Cf. A017162.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 10 2009