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%I #22 Sep 08 2022 08:44:57
%S 0,1,2,3,4,5,7,8,9,10,11,12,14,15,16,17,18,19,21,22,23,24,25,26,28,29,
%T 30,31,32,33,35,36,37,38,39,40,42,43,44,45,46,47,49,50,51,52,53,54,56,
%U 57,58,59,60,61,63,64,65,66,67,68,70,71,72,73,74,75,77
%N Numbers that are congruent to {0, 1, 2, 3, 4, 5} mod 7; a(n)=floor(7(n-1)/6).
%H Vincenzo Librandi, <a href="/A047368/b047368.txt">Table of n, a(n) for n = 1..1000</a>
%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+x^4+2*x^5) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 04 2011
%F From _Wesley Ivan Hurt_, Jun 15 2016: (Start)
%F a(n) = a(n-1) + a(n-6) - a(n-7) for n>7.
%F a(n) = (42*n-57-3*cos(Pi*n)-4*sqrt(3)*cos((4*n+1)*Pi/6)-12*sin((1-2*n)*Pi/6))/36.
%F a(6k) = 7k-2, 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 A047368:=n->(42*n-57-3*cos(Pi*n)-4*sqrt(3)*cos((4*n+1)*Pi/6)-12*sin((1-2*n)*Pi/6))/36: seq(A047368(n), n=1..100); # _Wesley Ivan Hurt_, Jun 15 2016
%t Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 4, 5}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 15 2016 *)
%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 4, 5, 7}, 100] (* _Vincenzo Librandi_, Jun 16 2016 *)
%o (PARI) a(n)=(n-1)*7\6 \\ _M. F. Hasler_, Oct 05 2014
%o (Magma) [n : n in [0..100] | n mod 7 in [0..5]]; // _Wesley Ivan Hurt_, Jun 15 2016
%Y Cf. A001068, A004773, A004777, A032766, A047226, A248375.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
%E Crossrefs and explicit formula in name added by _M. F. Hasler_, Oct 05 2014