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A046631 Number of cubic residues mod 3^n. 4
1, 3, 3, 7, 21, 57, 169, 507, 1515, 4543, 13629, 40881, 122641, 367923, 1103763, 3311287, 9933861, 29801577, 89404729, 268214187, 804642555, 2413927663, 7241782989, 21725348961, 65176046881, 195528140643, 586584421923 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n, arXiv:math/0604465 [math.NT], 2006-2016.

Index entries for linear recurrences with constant coefficients, signature (3,0,1,-3).

FORMULA

G.f.: (-3x^3-6x^2+1)/[(1-3x)(1-x^3)].

a(n) = A046530(3^n) = 4/3 +3^(n+1)/13 - (22*A049347(n)-16*A049347(n-1))/39 . - R. J. Mathar, Feb 27 2011

MAPLE

A049347 := proc(n) op( (n mod 3)+1, [1, -1, 0]) ; end proc:

A046631 := proc(n) 3^(n+1)/13+4/3-(22*A049347(n)-16*A049347(n-1))/39 ; end proc: # R. J. Mathar, Feb 27 2011

MATHEMATICA

LinearRecurrence[{3, 0, 1, -3}, {1, 3, 3, 7}, 27] (* Jean-Fran├žois Alcover, Nov 22 2017 *)

CROSSREFS

Sequence in context: A081486 A097334 A214496 * A100666 A262375 A232368

Adjacent sequences:  A046628 A046629 A046630 * A046632 A046633 A046634

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)