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A145209 Numbers x such that (x+67)^3-x^3 is a square. 1

%I

%S 9782,10111839727,10417116202859646,10731608941013901384311,

%T 11055596214932693950935000742,11389364664650780372372714547527967,

%U 11733209583865531835599714105766935834286,12087435181191042877051818694247666912610077671

%N Numbers x such that (x+67)^3-x^3 is a square.

%H Colin Barker, <a href="/A145209/b145209.txt">Table of n, a(n) for n = 1..166</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1030191,-1030191,1).

%F a(n+2) = 1030190*a(n+1)-a(n)+34511298.

%F a(n) = -(67/2)+(19631/4)*{[515095+124*sqrt(17255649)]^n+[515095-124*sqrt(17255649))^n}-(2077/1758)*sqrt(17255649)*{[515095-124 *sqrt(17255649)]^n-[515095+124*sqrt(17255649)]^n with n>=0. - _Paolo P. Lava_, Nov 25 2008

%F G.f.: 67*x*(147*x^2-515095*x-146) / ((x-1)*(x^2-1030190*x+1)). - _Colin Barker_, Oct 20 2014

%e The first relation is : (9782+67)^3-9782^3=139159^2.

%o (PARI) Vec(67*x*(147*x^2-515095*x-146)/((x-1)*(x^2-1030190*x+1)) + O(x^20)) \\ _Colin Barker_, Oct 20 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 04 2008, Oct 05 2008

%E Editing and a(8) from _Colin Barker_, Oct 20 2014

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Last modified January 17 18:14 EST 2020. Contains 330987 sequences. (Running on oeis4.)