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 A157842 a(n) = 3600*n^2 - 5599*n + 2177. 3

%I #15 Sep 08 2022 08:45:42

%S 178,5379,17780,37381,64182,98183,139384,187785,243386,306187,376188,

%T 453389,537790,629391,728192,834193,947394,1067795,1195396,1330197,

%U 1472198,1621399,1777800,1941401,2112202,2290203,2475404,2667805

%N a(n) = 3600*n^2 - 5599*n + 2177.

%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 A157844(n)^2-a(n)*A157843(n)^2=1.

%H Vincenzo Librandi, <a href="/A157842/b157842.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*(-178-4845*x-2177*x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{178,5379,17780},40]

%o (Magma) I:=[178, 5379, 17780]; [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) = 3600*n^2 - 5599*n + 2177.

%Y Cf. A157843, A157844.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 07 2009

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Last modified August 12 09:11 EDT 2024. Contains 375085 sequences. (Running on oeis4.)