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Numbers n such that there exists x in N with (x+67)^3-x^3=n^2.
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%I #14 Jul 11 2018 11:57:16

%S 139159,143360071051,147688111595890531,152146815684827106059839,

%T 156740128050204348280189648879,161472112515887870739083747272597171,

%U 166346955592585785428646481254476689943611

%N Numbers n such that there exists x in N with (x+67)^3-x^3=n^2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1030190,-1).

%F a(n+2) = 1030190*a(n+1)-a(n).

%F a(n) = 4489*A145210(n). - _Colin Barker_, Oct 19 2014

%F G.f.: -139159*x*(x-1) / (x^2-1030190*x+1). - _Colin Barker_, Oct 19 2014

%e a(1)= 139159 because the first relation is : (9782+67)^3-9782^3=139159^2.

%t LinearRecurrence[{1030190,-1},{139159,143360071051},20] (* _Harvey P. Dale_, Jul 11 2018 *)

%o (PARI) Vec(-139159*x*(x-1)/(x^2-1030190*x+1) + O(x^20)) \\ _Colin Barker_, Oct 19 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 04 2008