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%I #15 Sep 08 2022 08:44:56
%S 2,3,6,9,10,13,16,17,20,23,24,27,30,31,34,37,38,41,44,45,48,51,52,55,
%T 58,59,62,65,66,69,72,73,76,79,80,83,86,87,90,93,94,97,100,101,104,
%U 107,108,111,114,115,118,121,122,125,128,129,132,135,136,139,142
%N Numbers that are congruent to {2, 3, 6} mod 7.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F G.f.: x*(2+x+3*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F From _Wesley Ivan Hurt_, Jun 07 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (21*n-9+4*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-1, a(3k-1) = 7k-4, a(3k-2) = 7k-5. (End)
%p A047284:=n->(21*n-9+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047284(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t Table[(21*n-9+4*Sqrt[3]*Sin[2*n*Pi/3])/9, {n, 80}] (* _Wesley Ivan Hurt_, Jun 07 2016 *)
%o (Magma) [n : n in [1..150] | n mod 7 in [2, 3, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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