A145308 - OEIS

%I #12 Sep 08 2022 08:45:38

%S 19,8669719,3956010119119,1805135329365568219,

%T 823686861056211499347019,375849962071866284245677895519,

%U 171501089392493042372815103581763719,78256290091597510258728411110320270611619,35708501681204626036685798404088545017041209219

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

%H Vincenzo Librandi, <a href="/A145308/b145308.txt">Table of n, a(n) for n = 1..180</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (456302,-1).

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

%F G.f.: -19*x*(x-1) / (x^2-456302*x+1). - _Colin Barker_, Oct 19 2014

%e a(1)=19 because the first relation is : 98^3-97^3=79*19^2.

%t CoefficientList[Series[19 (1 - x)/(x^2 - 456302 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 19 2014 *)

%t LinearRecurrence[{456302,-1},{19,8669719},10] (* _Harvey P. Dale_, Dec 10 2015 *)

%o (PARI) Vec(-19*x*(x-1) / (x^2-456302*x+1) + O(x^20)) \\ _Colin Barker_, Oct 19 2014

%o (Magma) I:=[19, 8669719]; [n le 2 select I[n] else 456302*Self(n-1)-Self(n-2): n in [1..10]]; // _Vincenzo Librandi_, Oct 19 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 06 2008