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A047386 Numbers that are congruent to {0, 2, 5} mod 7.

%I A047386 #16 Sep 08 2022 08:44:57
%S A047386 0,2,5,7,9,12,14,16,19,21,23,26,28,30,33,35,37,40,42,44,47,49,51,54,
%T A047386 56,58,61,63,65,68,70,72,75,77,79,82,84,86,89,91,93,96,98,100,103,105,
%U A047386 107,110,112,114,117,119,121,124,126,128,131,133,135,138,140
%N A047386 Numbers that are congruent to {0, 2, 5} mod 7.
%H A047386 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047386 a(n+1) = 3*n-2*floor(n/3)-(n^2 mod 3). - _Gary Detlefs_, Mar 19 2010
%F A047386 G.f.: x^2*(2+3*x+2*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 05 2011
%F A047386 From _Wesley Ivan Hurt_, Jun 09 2016: (Start)
%F A047386 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047386 a(n) = (21*n-21+3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F A047386 a(3k) = 7k-2, a(3k-1) = 7k-5, a(3k-2) = 7k-7. (End)
%p A047386 seq(3*n-2*floor(n/3)-(n^2 mod 3), n=0..52); # _Gary Detlefs_, Mar 19 2010
%t A047386 Select[Range[0, 150], MemberQ[{0, 2, 5}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%o A047386 (Magma) [n : n in [0..150] | n mod 7 in [0, 2, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016
%Y A047386 Cf. A011655. [_Gary Detlefs_, Mar 19 2010]
%K A047386 nonn,easy
%O A047386 1,2
%A A047386 _N. J. A. Sloane_