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Numbers x such that there exists n in N : (x+79)^3-x^3=n^2.
1

%I #15 Jan 03 2024 23:44:20

%S 7663,3514673818,1603752710517223,731795569310933239378,

%T 333919781866113706302166783,152368264304339620843780392200938,

%U 69525943738264857888392566815788268343,31724827179505362919884965402334038047270498

%N Numbers x such that there exists n in N : (x+79)^3-x^3=n^2.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (456303,-456303,1).

%F a(n+2) = 456302*a(n+1)-a(n)+18023850.

%F G.f.: 79*x*(-97-228151*x+98*x^2) / ( (x-1)*(x^2-456302*x+1) ). - _R. J. Mathar_, Nov 27 2011

%F a(n) = 79*A145309(n). - _R. J. Mathar_, Nov 27 2011

%e a(1)=7663 because the first relation is : (7663+79)^3-7663^3=118579^2.

%t LinearRecurrence[{456303,-456303,1},{7663,3514673818,1603752710517223},20] (* _Harvey P. Dale_, Dec 14 2017 *)

%o (PARI) Vec(79*x*(-97-228151*x+98*x^2)/((x-1)*(x^2-456302*x+1)) + O(x^30)) \\ _Colin Barker_, Oct 18 2014

%Y Cf. A145306.

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 06 2008

%E Editing and additional term a(8) from _Colin Barker_, Oct 18 2014