A157855 - OEIS

%I #17 Sep 08 2022 08:45:42

%S 62697601,327628801,799920001,1479571201,2366582401,3460953601,

%T 4762684801,6271776001,7988227201,9912038401,12043209601,14381740801,

%U 16927632001,19680883201,22641494401,25809465601,29184796801,32767488001

%N 103680000n^2 - 46108800n + 5126401.

%C The identity (103680000*n^2-46108800*n+5126401)^2-(3600*n^2-1601*n +178)*(1728000*n-384240)^2=1 can be written as a(n)^2-A157853(n)*A157854(n)^2=1.

%H Vincenzo Librandi, <a href="/A157855/b157855.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*(-62697601-139535998*x-5126401*x^2)/(x-1)^3.

%t LinearRecurrence[{3,-3,1},{62697601,327628801,799920001},40]

%o (Magma) I:=[62697601, 327628801, 799920001]; [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 - 46108800*n + 5126401.

%Y Cf. A157853, A157854.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 08 2009