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%I
%S 14112,80539,201416,376743,606520,890747,1229424,1622551,2070128,
%T 2572155,3128632,3739559,4404936,5124763,5899040,6727767,7610944,
%U 8548571,9540648,10587175,11688152,12843579,14053456,15317783,16636560,18009787,19437464,20919591
%N a(n) = 27225*n^2 - 15248*n + 2135.
%C The identity (1482401250*n^2-830253600*n +116250751)^2-(27225*n^2-15248*n +2135) *(8984250*n -2515920)^2=1 can be written as A157788(n)^2-a(n)*A157787(n)^2=1.
%H Vincenzo Librandi, <a href="/A157786/b157786.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 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
%F G.f: x*(-14112-38203*x-2135*x^2)/(x-1)^3.
%t Table[27225*n^2-15248*n+2135,{n,50}] (* _Harvey P. Dale_, Nov 26 2010 *)
%o (Magma) I:=[14112, 80539, 201416]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..30]];
%o (PARI) a(n) = 27225*n^2-15248*n+2135.
%Y Cf. A157787, A157788.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 06 2009
%E More terms from _Harvey P. Dale_, Nov 26 2010
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