PROG
(MAGMAMagma) I:=[119071, 938449, 2535751]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
The OEIS is supported by the many generous donors to the OEIS Foundation.
(MAGMAMagma) I:=[119071, 938449, 2535751]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
editing
approved
aThis is the case s=21 and r=197 in the identity (2*(s^2*n-r)^2-1)^2 - (((s^2*n-r)^2-1)/s^2)*(2*s*(s^2*n-r))^2 = 1, where ((s^2*n-r) + ^2-1 )/s^2 is twice a squarean integer if r^2 == 1 (mod s^2). - Bruno Berselli, Apr 23 2018
approved
editing
editing
approved
a(n) + 1 is a twice of a square. - Bruno Berselli, Apr 23 2018
approved
editing
editing
approved
388962na(n) = 388962*n^2 - 347508n 347508*n + 77617.
The identity (388962*n^2 - 347508*n + 77617)^2 - (441*n^2 - 394*n + 88)*(18522*n - 8274)^2 = 1 can be written as a(n)^2 - A157734(n)*A157735(n)^2 = 1.
a(n) + 1 is a twice of a square. - Bruno Berselli, Apr 23 2018
G.f.: x*(119071 + 581236*x + 77617*x^2)/(1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(-119071-581236*x-77617*x^2)/(x-1)^3.
LinearRecurrence[{3, -3, 1}, {119071, 938449, 2535751}, 40]
approved
editing
editing
approved
Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&tstart=0">X^2-AY^2=1</a>
approved
editing
<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).