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

Offset

0,2

Links

Table of n, a(n) for n=0..19.

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).

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)

a(n) = A046530(8^n) = A046630(3n).

G.f.: ( 1-4*x ) / ( (1-8*x)*(1-x) ). (End)

a(n+1) = A226308(3n+2). - Philippe Deléham, Feb 24 2014

Mathematica

LinearRecurrence[{9, -8}, {1, 5}, 20] (* Jean-François Alcover, Jan 19 2019 *)

Crossrefs

Cf. A007583.

Sequence in context: A262410 A089303 A164595 * A091126 A066381 A078253

Adjacent sequences: A046633 A046634 A046635 * A046637 A046638 A046639

Keyword

nonn

Author

David W. Wilson

Status

approved