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A145334 Numbers x such that (x+43)^3-x^3 is a square. 1

%I #18 Jan 03 2024 23:45:35

%S 1118,38413663,1294925303334,43651931937700199,1471506624324949129678,

%T 49604488262342103224469903,1672167297852045675371932025174,

%U 56368759560987971454445725344870359,1900190883128737219877319726003648501438

%N Numbers x such that (x+43)^3-x^3 is a square.

%H Vincenzo Librandi, <a href="/A145334/b145334.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 (33711,-33711,1).

%F a(n+2) = 33710*a(n+1)-a(n)+724722.

%F G.f.: 43*x*(27*x^2-16855*x-26) / ((x-1)*(x^2-33710*x+1)). - _Colin Barker_, Oct 21 2014

%e a(1)=1118 because the first relation is : (1118+43)^3-1118^3=12943^2.

%t CoefficientList[Series[43 (27 x^2 - 16855 x - 26)/((x - 1) (x^2 - 33710 x + 1)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 21 2014 *)

%t LinearRecurrence[{33711,-33711,1},{1118,38413663,1294925303334},20] (* _Harvey P. Dale_, Feb 22 2017 *)

%o (PARI) Vec(43*x*(27*x^2-16855*x-26)/((x-1)*(x^2-33710*x+1)) + O(x^20)) \\ _Colin Barker_, Oct 21 2014

%o (Magma) I:=[1118,38413663,1294925303334]; [n le 3 select I[n] else 33711*Self(n-1)-33711*Self(n-2)+Self(n-3): n in [1..10]]; // _Vincenzo Librandi_, Oct 21 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 08 2008

%E Editing from _Colin Barker_, Oct 21 2014

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Last modified June 23 09:34 EDT 2024. Contains 373629 sequences. (Running on oeis4.)