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A047327 Numbers that are congruent to {3, 5, 6} mod 7.

%I A047327 #19 Sep 08 2022 08:44:56
%S A047327 3,5,6,10,12,13,17,19,20,24,26,27,31,33,34,38,40,41,45,47,48,52,54,55,
%T A047327 59,61,62,66,68,69,73,75,76,80,82,83,87,89,90,94,96,97,101,103,104,
%U A047327 108,110,111,115,117,118,122,124,125,129,131,132,136,138,139,143
%N A047327 Numbers that are congruent to {3, 5, 6} mod 7.
%C A047327 Also, numbers k such that (k^3+1)/7 is a nonnegative integer. - _Bruno Berselli_, Jan 16 2016
%H A047327 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047327 G.f.: x*(3+2*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 04 2011
%F A047327 From _Wesley Ivan Hurt_, Jun 07 2016: (Start)
%F A047327 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047327 a(n) = (21*n-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F A047327 a(3k) = 7k-1, a(3k-1) = 7k-2, a(3k-2) = 7k-4. (End)
%p A047327 A047327:=n->(21*n-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047327(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t A047327 Select[Range[0, 150], MemberQ[{3, 5, 6}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 07 2016 *)
%o A047327 (Magma) [n : n in [0..150] | n mod 7 in [3, 5, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K A047327 nonn,easy
%O A047327 1,1
%A A047327 _N. J. A. Sloane_