|
%I #24 Sep 08 2022 08:45:41
%S 1320,3048,4776,6504,8232,9960,11688,13416,15144,16872,18600,20328,
%T 22056,23784,25512,27240,28968,30696,32424,34152,35880,37608,39336,
%U 41064,42792,44520,46248,47976,49704,51432,53160,54888,56616,58344
%N a(n) = 1728*n - 408.
%C The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)*(1728*n-408)^2=1 can be written as A157267(n)^2-A157265(n)*a(n)^2=1 (see also the second comment in A157267). - _Vincenzo Librandi_, Jan 27 2012
%H Vincenzo Librandi, <a href="/A157266/b157266.txt">Table of n, a(n) for n = 1..10000</a>
%H Vincenzo Librandi, <a href="http://mathforum.org/kb/message.jspa?messageID=5785989&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). - _Vincenzo Librandi_, Jan 27 2012
%F G.f.: x*(1320+408*x)/(x-1)^2. - _Vincenzo Librandi_, Jan 27 2012
%F E.g.f.: 24*((72*x - 17)*exp(x) + 17). - _G. C. Greubel_, Feb 04 2018
%t LinearRecurrence[{2,-1},{1320,3048},40] (* _Vincenzo Librandi_, Jan 27 2012 *)
%t Table[1728n-408,{n,40}] (* _Harvey P. Dale_, Apr 18 2020 *)
%o (Magma) I:=[1320, 3048]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jan 27 2012
%o (PARI) for(n=1, 40, print1(1728*n - 408", ")); \\ _Vincenzo Librandi_, Jan 27 2012
%Y Cf. A157265, A157267.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 26 2009
|
