|
%I #21 Jan 03 2024 23:46:20
%S 1369,806341,475739821,280685688049,165604080209089,97706126637674461,
%T 57646449112147722901,34011307270040518837129,
%U 20066613642874793966183209,11839268037988858399529256181,6985148075799783580928294963581,4121225525453834323889294499256609
%N Numbers n such that there exists x in N with (x+37)^3-x^3=n^2.
%H Harvey P. Dale, <a href="/A145697/b145697.txt">Table of n, a(n) for n = 1..360</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (590,-1).
%F a(n+2) = 590*a(n+1)-a(n).
%F G.f.: -1369*x*(x-1) / (x^2-590*x+1). - _Colin Barker_, Oct 18 2014
%e a(1)=1369 because the first relation is (111+37)^3-111^3=1369^2.
%t LinearRecurrence[{590,-1},{1369,806341},20] (* _Harvey P. Dale_, Apr 10 2014 *)
%t CoefficientList[Series[1369 (1 - x)/(x^2 - 590 x + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 18 2014 *)
%o (PARI) Vec(-1369*x*(x-1)/(x^2-590*x+1) + O(x^20)) \\ _Colin Barker_, Oct 18 2014
%o (Magma) I:=[1369,806341]; [n le 2 select I[n] else 590*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Oct 18 2014
%K easy,nonn
%O 1,1
%A _Richard Choulet_, Oct 16 2008
%E Edited by _Colin Barker_, Oct 18 2014
| 