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%I #20 Sep 08 2022 08:44:57
%S 0,2,4,7,9,11,14,16,18,21,23,25,28,30,32,35,37,39,42,44,46,49,51,53,
%T 56,58,60,63,65,67,70,72,74,77,79,81,84,86,88,91,93,95,98,100,102,105,
%U 107,109,112,114,116,119,121,123,126,128,130,133,135,137,140,142
%N Numbers that are congruent to {0, 2, 4} mod 7.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(n+1) = floor(n/3)+2*n. - _Gary Detlefs_, Mar 27 2010
%F G.f.: x^2*(2+2*x+3*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%F a(n) = n + floor(4*(n-1)/3) - 1. - _Arkadiusz Wesolowski_, Sep 18 2012
%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (21*n-24-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-3, a(3k-1) = 7k-5, a(3k-2) = 7k-7. (End)
%p seq(floor(n/3)+2*n, n=0..52); # _Gary Detlefs_, Mar 27 2010
%t Select[Range[0, 150], MemberQ[{0, 2, 4}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [0, 2, 4]]; // _Wesley Ivan Hurt_, Jun 10 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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