A157844 - OEIS

%I #13 Sep 08 2022 08:45:42

%S 5126401,154915201,512064001,1076572801,1848441601,2827670401,

%T 4014259201,5408208001,7009516801,8818185601,10834214401,13057603201,

%U 15488352001,18126460801,20971929601,24024758401,27284947201,30752496001

%N 103680000n^2 - 161251200n + 62697601.

%C The identity (103680000*n^2-161251200*n+62697601)^2-(3600*n^2-5599*n+2177)*(1728000*n-1343760)^2=1 can be written as a(n)^2-A157842(n)*A157843(n)^2=1.

%H Vincenzo Librandi, <a href="/A157844/b157844.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).

%F G.f.: x*(-5126401-139535998*x-62697601*x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{5126401,154915201,512064001},40]

%o (Magma) I:=[5126401, 154915201, 512064001]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

%o (PARI) a(n) = 103680000*n^2 - 161251200*n + 62697601.

%Y Cf. A157842, A157843.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 07 2009