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A145720 Numbers x such that there exists n in N with (x+1)^3-x^3=127*n^2. 3

%I

%S 6,13201,26799038,54402034953,110436104156566,224185237035795041,

%T 455095920746559777678,923844494930279312892313,

%U 1875403869612546258611618726,3807068931468973974702273122481,7728348055478147556099355827018718,15688542745551708069907717626574876073

%N Numbers x such that there exists n in N with (x+1)^3-x^3=127*n^2.

%H Vincenzo Librandi, <a href="/A145720/b145720.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2031,-2031,1).

%F a(n+2) = 2030*a(n+1)-a(n)+1014.

%F a(n) = -(1/2)+(13/4)*{[1015+52*sqrt(381)]^n+[1015-52*sqrt(381)])^n}+(1/6)*sqrt(381)*{[1015+52*sqrt(381)]^n-[1015-52*sqrt(381)]^n} with n>=0. - _Paolo P. Lava_, Nov 25 2008

%F a(n) = A145718(n)/127. - _Colin Barker_, Oct 18 2014

%F G.f.: x*(7*x^2-1015*x-6) / ((x-1)*(x^2-2030*x+1)). - _Colin Barker_, Oct 18 2014

%e a(1)=6 because the first relation is 7^3-6^3=127*1^2.

%t CoefficientList[Series[(7 x^2 - 1015 x - 6)/((x - 1) (x^2 - 2030 x + 1)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 18 2014 *)

%o (PARI) Vec(x*(7*x^2-1015*x-6)/((x-1)*(x^2-2030*x+1)) + O(x^20)) \\ _Colin Barker_, Oct 18 2014

%o (MAGMA) I:=[6,13201]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2)+1014: n in [1..20]]; // _Vincenzo Librandi_, Oct 18 2014

%Y Cf. A145718.

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 16 2008

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

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Last modified December 5 05:51 EST 2020. Contains 338944 sequences. (Running on oeis4.)