A046632 Number of cubic residues mod 4^n.

1, 3, 10, 37, 147, 586, 2341, 9363, 37450, 149797, 599187, 2396746, 9586981, 38347923, 153391690, 613566757, 2454267027, 9817068106, 39268272421, 157073089683, 628292358730, 2513169434917, 10052677739667, 40210710958666

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,0,1,-4)

Programs

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

Mathematica

LinearRecurrence[{4,0,1,-4},{1,3,10,37},40] (* Vincenzo Librandi, Jun 22 2012 *)

Formula

G.f.: (-4x^3 - 2x^2 - x+1)/((1-4x)*(1-x^3)).

a(n) = A046530(4^n) = A046630(2n). - R. J. Mathar, Feb 27 2011

a(n) = 4*a(n-1) + a(n-3) - 4*a(n-4). - Vincenzo Librandi, Jun 22 2012