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%I #16 Sep 08 2022 08:44:56
%S 0,5,6,7,12,13,14,19,20,21,26,27,28,33,34,35,40,41,42,47,48,49,54,55,
%T 56,61,62,63,68,69,70,75,76,77,82,83,84,89,90,91,96,97,98,103,104,105,
%U 110,111,112,117,118,119,124,125,126,131,132,133,138,139,140
%N Numbers that are congruent to {0, 5, 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*(5+x+x^2) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 03 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-9-8*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-1, a(3k-1) = 7k-2, a(3k-2) = 7k-7. (End)
%p A047320:=n->(21*n-9-8*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047320(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t Select[Range[0,200], MemberQ[{0,5,6}, Mod[#,7]]&] (* _Harvey P. Dale_, May 25 2012 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [0, 5, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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