%I #29 Sep 08 2022 08:44:56
%S 0,1,2,3,4,6,7,8,9,10,11,13,14,15,16,17,18,20,21,22,23,24,25,27,28,29,
%T 30,31,32,34,35,36,37,38,39,41,42,43,44,45,46,48,49,50,51,52,53,55,56,
%U 57,58,59,60,62,63,64,65,66,67,69,70,71,72,73,74,76
%N Numbers that are congruent to {0, 1, 2, 3, 4, 6} mod 7.
%C Complement of A017041. - _Michel Marcus_, Sep 08 2015
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F G.f.: x^2*(1+x+x^2+x^3+2*x^4+x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F From _Wesley Ivan Hurt_, Sep 07 2015: (Start)
%F a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F a(n) = n + 1 + floor((n-2)/6) - ceiling((n-1)/6) + floor((n-1)/6) - ceiling(n/6) + floor(n/6). (End)
%F From _Wesley Ivan Hurt_, Jun 15 2016: (Start)
%F a(n) = (42*n - 51 + 3*cos(n*Pi) + 4*sqrt(3)*cos((1-4*n)*Pi/6) + 12*sin((1+2*n)*Pi/6))/36.
%F a(6k) = 7k-1, a(6k-1) = 7k-3, a(6k-2) = 7k-4, a(6k-3) = 7k-5, a(6k-4) = 7k-6, a(6k-5) = 7k-7. (End)
%p A047303:=n->n+1+floor((n-2)/6)-ceil((n-1)/6)+floor((n-1)/6)-ceil(n/6)+floor(n/6): seq(A047303(n), n=1..100); # _Wesley Ivan Hurt_, Sep 07 2015
%t Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4, 6}, Mod[#, 7]] &] (* _Vincenzo Librandi_, Sep 08 2015 *)
%t LinearRecurrence[{1,0,0,0,0,1,-1},{0,1,2,3,4,6,7},80] (* _Harvey P. Dale_, Sep 24 2016 *)
%o (Magma) [n: n in [0..100] | n mod 7 in [0..4] cat [6]]; // _Vincenzo Librandi_, Sep 08 2015
%Y Cf. A017041 (7n+5).
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Vincenzo Librandi_, Sep 08 2015