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%I #23 Sep 08 2022 08:44:57
%S 0,1,3,7,8,10,14,15,17,21,22,24,28,29,31,35,36,38,42,43,45,49,50,52,
%T 56,57,59,63,64,66,70,71,73,77,78,80,84,85,87,91,92,94,98,99,101,105,
%U 106,108,112,113,115,119,120,122,126,127,129,133,134,136,140
%N Numbers that are congruent to {0, 1, 3} mod 7.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F Partial sums of (0, 1, 2, 4, 1, 2, 4, 1, 2, 4, ...). - _Gary W. Adamson_, Jun 19 2008
%F G.f.: x^2*(1+2*x+4*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 04 2011
%F From _Wesley Ivan Hurt_, Jun 08 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (21*n-30-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-4, a(3k-1) = 7k-6, a(3k-2) = 7k-7. (End)
%p A047357:=n->(21*n-30-6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047357(n), n=1..100); # _Wesley Ivan Hurt_, Jun 08 2016
%t Select[Range[0, 200], Mod[#, 7] == 0 || Mod[#, 7] == 1 || Mod[#, 7] == 3 &] (* _Vladimir Joseph Stephan Orlovsky_, Jul 10 2011 *)
%t Select[Range[0,200], MemberQ[{0,1,3}, Mod[#,7]]&] (* _Harvey P. Dale_, Nov 30 2012 *)
%t Accumulate[PadRight[{0},70,{4,1,2}]] (* _Harvey P. Dale_, Aug 16 2021 *)
%o (Magma) [n : n in [0..150] | n mod 7 in [0, 1, 3]]; // _Wesley Ivan Hurt_, Jun 08 2016
%Y Cf. A047360.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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