%I #15 Jan 06 2024 00:57:48
%S 2,757,228762,69085517,20863597522,6300737366277,1902801821018282,
%T 574639849210155037,173539331659645803042,52408303521363822363797,
%U 15827134124120214708063802,4779742097180783478012904557,1443466286214472490145189112562
%N Numbers x such that there exists n in N : (x+1)^3-x^3=19*n^2.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (303,-303,1).
%F a(n+2) = 302*a(n+1)-a(n)+150.
%F G.f.: x*(-2-151*x+3*x^2) / ( (x-1)*(x^2-302*x+1) ). - _R. J. Mathar_, Nov 27 2011
%e a(1)=2 because 3^3-2^3=19*1.
%t CoefficientList[Series[(-2 - 151*x + 3*x^2)/((x - 1)*(x^2 - 302*x + 1)), {x, 0, 15}], x] (* _Wesley Ivan Hurt_, Sep 04 2022 *)
%o (PARI) Vec(x*(-2-151*x+3*x^2)/((x-1)*(x^2-302*x+1)) + O(x^30)) \\ _Colin Barker_, Oct 18 2014
%Y Cf. A145123.
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 02 2008
%E Editing and more terms from _Colin Barker_, Oct 18 2014