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%I #16 Sep 08 2022 08:44:56
%S 3,4,6,10,11,13,17,18,20,24,25,27,31,32,34,38,39,41,45,46,48,52,53,55,
%T 59,60,62,66,67,69,73,74,76,80,81,83,87,88,90,94,95,97,101,102,104,
%U 108,109,111,115,116,118,122,123,125,129,130,132,136,137,139,143
%N Numbers that are congruent to {3, 4, 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*(3+x+2*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-3-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-1, a(3k-1) = 7k-3, a(3k-2) = 7k-4. (End)
%p A047296:=n->(21*n-3-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047296(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t LinearRecurrence[{1,0,1,-1}, {3,4,6,10}, 60] (* _Harvey P. Dale_, Apr 27 2015 *)
%o (Magma) [n : n in [1..150] | n mod 7 in [3, 4, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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