A046636 Number of cubic residues mod 8^n.
1, 5, 37, 293, 2341, 18725, 149797, 1198373, 9586981, 76695845, 613566757, 4908534053, 39268272421, 314146179365, 2513169434917, 20105355479333, 160842843834661, 1286742750677285, 10293942005418277, 82351536043346213, 658812288346769701, 5270498306774157605, 42163986454193260837
Offset: 0
Links
- Ralf Stephan, Prove or disprove: 100 conjectures from the OEIS, arXiv:math/0409509 [math.CO], 2004.
- E. Wilmer and O. Schirokauer, A note on Stephan's conjecture 25, 2004. [broken link]
- E. Wilmer and O. Schirokauer, A note on Stephan's conjecture 25, 2004. [cached copy]
- Index entries for linear recurrences with constant coefficients, signature (9,-8).
Programs
-
Mathematica
LinearRecurrence[{9, -8}, {1, 5}, 20] (* Jean-François Alcover, Jan 19 2019 *)
Formula
a(n) = (4*8^n + 3)/7.
a(n) = 8*a(n-1) - 3 (with a(0)=1). - Vincenzo Librandi, Nov 18 2010
From R. J. Mathar, Feb 28 2011: (Start)
G.f.: (1-4*x)/((1-8*x)*(1-x)). (End)
a(n+1) = A226308(3*n+2). - Philippe Deléham, Feb 24 2014
From Elmo R. Oliveira, Apr 03 2025: (Start)
E.g.f.: exp(x)*(4*exp(7*x) + 3)/7.
a(n) = 9*a(n-1) - 8*a(n-2).
a(n) = A047853(n+1)/2. (End)
Extensions
More terms from Elmo R. Oliveira, Apr 03 2025