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%I #21 Apr 08 2024 06:57:05
%S 31,31935859,32900002583179,33893253661133238151,
%T 34916490989129950608195511,35970619852057890563395800238939,
%U 37056572865356601788515589497544372899,38175310800125746976658817253911841716581871,39327823433144486705018790345018924628507933312591
%N Numbers n such that there exists x in N : (x+1)^3-x^3=67*n^2.
%H Vincenzo Librandi, <a href="/A145210/b145210.txt">Table of n, a(n) for n = 1..170</a>
%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) = A145207(n)/4489. - _Colin Barker_, Oct 19 2014
%F G.f.: -31*x*(x-1) / (x^2-1030190*x+1). - _Colin Barker_, Oct 19 2014
%F a(n) = A145205(n)/134. - _Hugo Pfoertner_, Apr 08 2024
%e a(1)=31 because the first relation is : 147^3-146^3=67*31^2.
%t CoefficientList[Series[31 (1 - x)/(x^2 - 1030190 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 19 2014 *)
%t LinearRecurrence[{1030190,-1},{31,31935859},10] (* _Harvey P. Dale_, Aug 11 2021 *)
%o (PARI) Vec(-31*x*(x-1)/(x^2-1030190*x+1) + O(x^20)) \\ _Colin Barker_, Oct 19 2014
%o (Magma) I:=[31,31935859]; [n le 2 select I[n] else 1030190*Self(n-1)-Self(n-2): n in [1..10]]; // _Vincenzo Librandi_, Oct 19 2014
%Y Cf. A145205, A145207.
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 04 2008
%E Editing and more terms from _Colin Barker_, Oct 19 2014
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