A145123 - OEIS

%I #18 Jan 06 2024 00:57:45

%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.

%H Vincenzo Librandi, <a href="/A145123/b145123.txt">Table of n, a(n) for n = 1..100</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (302,-1).

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

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

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

%t CoefficientList[Series[(1 - x)/(1 - 302 x + x^2), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 18 2014 *)

%o (PARI) Vec(-x*(-1+x)/(1-302*x+x^2) + O(x^30)) \\ _Colin Barker_, Oct 18 2014

%Y Cf. A145124.

%K easy,nonn

%O 1,2

%A _Richard Choulet_, Oct 02 2008

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