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%I #25 Sep 08 2022 08:45:42
%S 16471,86048,210075,388552,621479,908856,1250683,1646960,2097687,
%T 2602864,3162491,3776568,4445095,5168072,5945499,6777376,7663703,
%U 8604480,9599707,10649384,11753511,12912088,14125115,15392592,16714519
%N a(n) = 27225*n^2 - 12098*n + 1344.
%C The identity(1482401250*n^2-658736100*n+73180801)^2-(27225*n^2-12098*n+1344)*(8984250*n-1996170)^2=1 can be written as A157798(n)^2-a(n)*A157797(n)^2=1.
%H Vincenzo Librandi, <a href="/A157796/b157796.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(16471 + 36635*x + 1344*x^2)/(1 - x)^3.
%F a(1)=16471, a(2)=86048, a(3)=210075; for n>3, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Jul 02 2011
%t Table[27225 n^2 - 12098 n + 1344, {n, 25}] (* _Harvey P. Dale_, Feb 20 2011 *)
%t LinearRecurrence[{3, -3, 1}, {16471, 86048, 210075}, 25] (* _Harvey P. Dale_, Jul 02 2011 *)
%o (Magma) I:=[16471, 86048, 210075]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]];
%o (PARI) a(n)=27225*n^2-12098*n+1344;
%Y Cf. A157797, A157798.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
%E Edited by _M. F. Hasler_, Oct 08 2014
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