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%I #16 Jan 06 2024 00:58:14
%S 16129,32725741,66433238101,134859440619289,273764598023918569,
%T 555741999129114075781,1128155984467503549916861,
%U 2290156092727033077217152049,4649015740079892679247268742609,9437499662206089411838878330344221,19158119665262621426140243763330026021
%N Numbers n such that there exists x in N with (x+127)^3-x^3=n^2.
%H Vincenzo Librandi, <a href="/A145717/b145717.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2030,-1).
%F a(n+2) = 2030*a(n+1)-a(n).
%F a(n) = A145721(n)*16129. - _Colin Barker_, Oct 20 2014
%F G.f.: -16129*x*(x-1) / (x^2-2030*x+1). - _Colin Barker_, Oct 20 2014
%e a(1)=16129 because the first relation is (762+127)^3-762^3=16129^2.
%t CoefficientList[Series[16129 (1 - x)/(x^2 - 2030 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 20 2014 *)
%o (PARI) Vec(-16129*x*(x-1)/(x^2-2030*x+1) + O(x^20)) \\ _Colin Barker_, Oct 20 2014
%o (Magma) I:=[16129,32725741]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Oct 20 2014
%Y Cf. A145721.
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 16 2008
%E Editing and more terms from _Colin Barker_, Oct 20 2014
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