cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A046631 Number of cubic residues mod 3^n.

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%I A046631 #29 Feb 06 2024 02:08:59
%S A046631 1,3,3,7,21,57,169,507,1515,4543,13629,40881,122641,367923,1103763,
%T A046631 3311287,9933861,29801577,89404729,268214187,804642555,2413927663,
%U A046631 7241782989,21725348961,65176046881,195528140643,586584421923
%N A046631 Number of cubic residues mod 3^n.
%H A046631 S. R. Finch and Pascal Sebah, <a href="https://arxiv.org/abs/math/0604465">Squares and Cubes Modulo n</a>, arXiv:math/0604465 [math.NT], 2006-2016.
%H A046631 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,1,-3).
%F A046631 G.f.: (-3*x^3-6*x^2+1)/((1-3*x)*(1-x^3)).
%F A046631 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
%p A046631 A049347 := proc(n) op( (n mod 3)+1,[1,-1,0]) ; end proc:
%p A046631 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
%t A046631 LinearRecurrence[{3, 0, 1, -3}, {1, 3, 3, 7}, 27] (* _Jean-François Alcover_, Nov 22 2017 *)
%K A046631 nonn,easy
%O A046631 0,2
%A A046631 _David W. Wilson_