cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A145720 #15 Jan 06 2024 00:58:39
%S A145720 6,13201,26799038,54402034953,110436104156566,224185237035795041,
%T A145720 455095920746559777678,923844494930279312892313,
%U A145720 1875403869612546258611618726,3807068931468973974702273122481,7728348055478147556099355827018718,15688542745551708069907717626574876073
%N A145720 Numbers x such that there exists n in N with (x+1)^3-x^3=127*n^2.
%H A145720 Vincenzo Librandi, <a href="/A145720/b145720.txt">Table of n, a(n) for n = 1..200</a>
%H A145720 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2031,-2031,1).
%F A145720 a(n+2) = 2030*a(n+1)-a(n)+1014.
%F A145720 a(n) = A145718(n)/127. - _Colin Barker_, Oct 18 2014
%F A145720 G.f.: x*(7*x^2-1015*x-6) / ((x-1)*(x^2-2030*x+1)). - _Colin Barker_, Oct 18 2014
%e A145720 a(1)=6 because the first relation is 7^3-6^3=127*1^2.
%t A145720 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 A145720 (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 A145720 (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 A145720 Cf. A145718.
%K A145720 easy,nonn
%O A145720 1,1
%A A145720 _Richard Choulet_, Oct 16 2008
%E A145720 Editing and more terms from _Colin Barker_, Oct 18 2014