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Numbers x such that there exists n in N with (x+1)^3-x^3=37*n^2.
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%I #14 Jan 17 2024 07:48:26

%S 3,2068,1220411,720040716,424822802323,250644733330148,

%T 147879967841985291,87248930382037991836,51476721045434573198243,

%U 30371178167876016148971828,17918943642325804093320180571,10572146377794056539042757565356,6237548443954851032231133643379763

%N Numbers x such that there exists n in N with (x+1)^3-x^3=37*n^2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (591,-591,1).

%F a(n+2) = 590*a(n+1)-a(n)+294.

%F G.f.: x*(4*x^2-295*x-3) / ((x-1)*(x^2-590*x+1)). - _Colin Barker_, Oct 18 2014

%t LinearRecurrence[{591, -591, 1}, {3, 2068, 1220411}, 15] (* _Paolo Xausa_, Jan 17 2024 *)

%o (PARI) Vec(x*(4*x^2-295*x-3)/((x-1)*(x^2-590*x+1)) + O(x^20)) \\ _Colin Barker_, Oct 18 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 16 2008

%E Editing and more terms from _Colin Barker_, Oct 18 2014