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%I #25 Sep 08 2022 08:44:57
%S 1,3,4,8,10,11,15,17,18,22,24,25,29,31,32,36,38,39,43,45,46,50,52,53,
%T 57,59,60,64,66,67,71,73,74,78,80,81,85,87,88,92,94,95,99,101,102,106,
%U 108,109,113,115,116,120,122,123,127,129,130,134,136,137,141
%N Numbers that are congruent to {1, 3, 4} mod 7.
%C Also, numbers n such that kronecker(n+2, 7) = -1. - _M. F. Hasler_, Mar 15 2013
%H Harvey P. Dale, <a href="/A047343/b047343.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F G.f.: x*(1+2*x+x^2+3*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 04 2011
%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-18-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-3, a(3k-1) = 7k-4, a(3k-2) = 7k-6. (End)
%p A047343:=n->(21*n-18-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047343(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t Flatten[Table[{7n + 1, 7n + 3, 7n + 4}, {n, 0, 19}]] (* _Alonso del Arte_, Mar 15 2013 *)
%t LinearRecurrence[{1,0,1,-1},{1,3,4,8},90] (* _Harvey P. Dale_, Aug 07 2021 *)
%o (PARI) A047343(n)=n\3*7+[-3,1,3][n%3+1] \\ _M. F. Hasler_, Mar 15 2013
%o (PARI) for(k=1,200,kronecker(k+2,7)==-1 & print1(k",")) \\ For illustrative purpose of the comment. - _M. F. Hasler_, Mar 15 2013
%o (Magma) [n : n in [0..150] | n mod 7 in [1, 3, 4]]; // _Wesley Ivan Hurt_, Jun 10 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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