A046637 Number of cubic residues mod 9^n.

1, 3, 21, 169, 1515, 13629, 122641, 1103763, 9933861, 89404729, 804642555, 7241782989, 65176046881, 586584421923, 5279259797301, 47513338175689, 427620043581195, 3848580392230749, 34637223530076721, 311735011770690483

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,0,1,-9)

Formula

a(n) = A046530(9^n) = A046631(2n). G.f. ( 1-6*x-6*x^2-21*x^3 ) / ( (x-1)*(9*x-1)*(1+x+x^2) ). - R. J. Mathar, Feb 28 2011

If n>=1, a(n) = 9*a(n-1) -6 if n is not a multiple of 3, otherwise a(n) = 9*a(n-1) -20. - Vincenzo Librandi, Mar 18 2011

Mathematica

LinearRecurrence[{9, 0, 1, -9}, {1, 3, 21, 169}, 30] (* Harvey P. Dale, Oct 09 2017 *)

Crossrefs

Sequence in context: A371771 A214391 A370284 * A220103 A132805 A372459

Adjacent sequences: A046634 A046635 A046636 * A046638 A046639 A046640

Keyword

nonn,easy

Author

David W. Wilson

Status

approved