A157369 - OEIS

%I #22 Sep 08 2022 08:45:42

%S 70,413,756,1099,1442,1785,2128,2471,2814,3157,3500,3843,4186,4529,

%T 4872,5215,5558,5901,6244,6587,6930,7273,7616,7959,8302,8645,8988,

%U 9331,9674,10017,10360,10703,11046,11389,11732,12075,12418,12761,13104,13447

%N a(n) = 343*n - 273.

%C The identity (2401*n^2-3822*n+1520)^2-(49*n^2-78*n+31)*(343*n-273)^2=1 can be written as A157370(n)^2-A157368(n)*a(n)^2=1.

%H Vincenzo Librandi, <a href="/A157369/b157369.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 G.f: x*(70+273*x)/(1-x)^2.

%F E.g.f.: 7*(39 - (39-49*x)*exp(x)). - _G. C. Greubel_, Feb 02 2018

%t LinearRecurrence[{3,-3,1},{70,413,756},40]

%t 343Range[40]-273  (* _Harvey P. Dale_, Mar 13 2011 *)

%o (Magma) I:=[70, 413, 756]; [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)= 343*n-273.

%Y Cf. A157368, A157370.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 28 2009