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 A145123 Numbers n such that there exists x in N : (x+1)^3-x^3=19*n^2 2

%I

%S 1,301,90901,27451801,8290353001,2503659154501,756096774306301,

%T 228338722181348401,68957538001992910801,20824948137879677713501,

%U 6289065380101660676566501,1899276919842563644645369801

%N Numbers n such that there exists x in N : (x+1)^3-x^3=19*n^2

%C a(1)=1 because 3^3-2^3=19*1

%H <a href="/index/Rec#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (302,-1).

%F a(n+2)=302*a(n+1)-a(n)

%F a(n)=(1/2)*{[151+20*sqrt(57)]^n+[151-20*sqrt(57)]^n}-(5/76)*sqrt(57)*{[151-20 *sqrt(57)]^n-[151+20*sqrt(57)]^n}, with n>=0 [From _Paolo P. Lava_, Nov 25 2008]

%F G.f. -x*(-1+x) / ( 1-302*x+x^2 ). - R. J. Mathar, Nov 27 2011

%Y Cf. A145124.

%K easy,nonn

%O 1,2

%A _Richard Choulet_, Oct 02 2008

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