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 A145698 Numbers x such that (x+37)^3-x^3 is a square. 0

%I #13 Jan 03 2024 23:46:25

%S 111,76516,45155207,26641506492,15718443685951,9273855133215476,

%T 5471558810153455767,3228210424135405697932,1904638678681079208334991,

%U 1123733592211412597511957636

%N Numbers x such that (x+37)^3-x^3 is a square.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (591,-591,1).

%F a(n+2)=590*a(n+1)-a(n)+10868.

%e a(1)=111 because the first relation is (111+37)^3-111^3=1369^2.

%t CoefficientList[Series[(37 (-3-295 x+4 x^2))/(-1+591 x-591 x^2+x^3),{x,0,10}],x] (* _Harvey P. Dale_, Feb 20 2011 *)

%o (PARI) Vec((111*x^2 - 65749*x + 76516)/(-x^3 + 591*x^2 - 591*x + 1)+O(x^99)) \\ _Charles R Greathouse IV_, May 28 2014

%K nonn,easy

%O 1,1

%A _Richard Choulet_, Oct 16 2008

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Last modified March 5 02:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)