|
%I #23 Mar 27 2024 13:32:32
%S 1,3,10,37,147,586,2341,9363,37450,149797,599187,2396746,9586981,
%T 38347923,153391690,613566757,2454267027,9817068106,39268272421,
%U 157073089683,628292358730,2513169434917,10052677739667,40210710958666
%N Number of cubic residues mod 4^n.
%H Vincenzo Librandi, <a href="/A046632/b046632.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4)
%F G.f.: (-4x^3 - 2x^2 - x+1)/((1-4x)*(1-x^3)).
%F a(n) = A046530(4^n) = A046630(2n). - _R. J. Mathar_, Feb 27 2011
%F a(n) = 4*a(n-1) + a(n-3) - 4*a(n-4). - _Vincenzo Librandi_, Jun 22 2012
%t LinearRecurrence[{4,0,1,-4},{1,3,10,37},40] (* _Vincenzo Librandi_, Jun 22 2012 *)
%o (Magma) I:=[1, 3, 10, 37]; [n le 4 select I[n] else 4*Self(n-1)+Self(n-3)-4*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Jun 22 2012
%K nonn,easy
%O 0,2
%A _David W. Wilson_
|
