|
%I #18 Sep 08 2022 08:45:42
%S 91,30464,115287,254560,448283,696456,999079,1356152,1767675,2233648,
%T 2754071,3328944,3958267,4642040,5380263,6172936,7020059,7921632,
%U 8877655,9888128,10953051,12072424,13246247,14474520,15757243,17094416
%N a(n) = 27225*n^2 - 51302*n + 24168.
%C The identity (1482401250*n^2-2793393900*n+1315947601)^2-(27225*n^2-51302*n+24168)*(8984250*n-8464830)^2=1 can be written as A157804(n)^2-a(n)*A157803(n)^2=1.
%H Vincenzo Librandi, <a href="/A157802/b157802.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*(91 + 30191*x + 24168*x^2)/(1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%t LinearRecurrence[{3, -3, 1}, {91, 30464, 115287}, 40]
%o (Magma) I:=[91, 30464, 115287]; [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 - 51302*n + 24168;
%Y Cf. A157803, A157804.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Mar 07 2009
|
