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%I #18 Sep 08 2022 08:44:57
%S 1,2,5,8,9,12,15,16,19,22,23,26,29,30,33,36,37,40,43,44,47,50,51,54,
%T 57,58,61,64,65,68,71,72,75,78,79,82,85,86,89,92,93,96,99,100,103,106,
%U 107,110,113,114,117,120,121,124,127,128,131,134,135,138,141
%N Numbers that are congruent to {1, 2, 5} 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*(1+x+3*x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 05 2011
%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>1.
%F a(n) = 7*n/3-2+4*sin(2*n*Pi/3)/(3*sqrt(3)).
%F a(3k) = 7k-2, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)
%p A047387:=n->7*n/3-2+4*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047387(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t Select[Range[200], MemberQ[{1,2,5}, Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,1,-1},{1,2,5,8},90] (* _Harvey P. Dale_, Jun 05 2014 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [1, 2, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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