A157432 - OEIS

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

%S 648,712,776,840,904,968,1032,1096,1160,1224,1288,1352,1416,1480,1544,

%T 1608,1672,1736,1800,1864,1928,1992,2056,2120,2184,2248,2312,2376,

%U 2440,2504,2568,2632,2696,2760,2824,2888,2952,3016,3080,3144,3208,3272,3336

%N 64n + 584.

%C The identity (128*n^2+2336*n+10657)^2-(4*n^2+73*n+333)*(64*n+584)^2=1 can be written as A157433(n)^2-A157431(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157432/b157432.txt">Table of n, a(n) for n = 1..10000</a>

%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5773147&amp;tstart=0">X^2-AY^2=1</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*a(n-1)-a(n-2).

%F G.f.: x*(648-584x)/(1-x)^2.

%t LinearRecurrence[{2,-1},{648,712},50]

%t 64*Range[50]+584 (* _Harvey P. Dale_, Sep 09 2012 *)

%o (Magma) I:=[648, 712]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];

%o (PARI) a(n) = 64*n + 584.

%Y Cf. A157431, A157433.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 01 2009