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A145336 Numbers x such that there exists n in N : (x+1)^3-x^3=43*n^2. 2


%S 26,893341,30114541938,1015161207853493,34221084286626723946,

%T 1153592750287025656383021,38887611577954550590044930818,

%U 1310901385139255150103388961508613,44190485654156679532030691302410430266,1489661270090720281885499453700866642775101

%N Numbers x such that there exists n in N : (x+1)^3-x^3=43*n^2.

%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)+16854.

%F a(n) = -(1/2)+(53/4)*{[16855+1484*sqrt(129)]^n+[16855-1484*sqrt(129)]^n}-(7/6)*sqrt(129)*{[16855-1484*sqrt(129)]^n- [16855+1484*sqrt(129)]^n} with n>=0. - _Paolo P. Lava_, Nov 25 2008

%F G.f.: x*(27*x^2-16855*x-26) / ((x-1)*(x^2-33710*x+1)). - _Colin Barker_, Oct 18 2014

%e a(1)=26 because the first relation is : 27^3-26^3=43*7^2.

%o (PARI) Vec(x*(27*x^2-16855*x-26)/((x-1)*(x^2-33710*x+1)) + O(x^20)) \\ _Colin Barker_, Oct 18 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 08 2008

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

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)