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A047342 Numbers that are congruent to {0, 3, 4} mod 7.

%I A047342 #28 Sep 08 2022 08:44:57
%S A047342 0,3,4,7,10,11,14,17,18,21,24,25,28,31,32,35,38,39,42,45,46,49,52,53,
%T A047342 56,59,60,63,66,67,70,73,74,77,80,81,84,87,88,91,94,95,98,101,102,105,
%U A047342 108,109,112,115,116,119,122,123,126,129,130,133,136,137,140
%N A047342 Numbers that are congruent to {0, 3, 4} mod 7.
%C A047342 Record values in A168223: a(n) = A168223(A168224(n)) and A168223(m) < a(n) for m < A168224(n). - _Reinhard Zumkeller_, Nov 20 2009
%C A047342 Also: Numbers n such that kronecker(n^2-4,7) = -1. - _M. F. Hasler_, Mar 14 2013
%H A047342 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047342 G.f.: x(3+x+3x^2)/((1-x)^2*(1+x+x^2)). - _R. J. Mathar_, Sep 17 2008
%F A047342 a(n) = a(n-1) + a(n-3) - a(n-4), n>4. - _Vincenzo Librandi_, Mar 24 2011
%F A047342 From _Wesley Ivan Hurt_, Jun 13 2016: (Start)
%F A047342 a(n) = (21*n-21-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.
%F A047342 a(3k) = 7k-3, a(3k-1) = 7k-4, a(3k-2) = 7k-7. (End)
%p A047342 A047342:=n->(21*n-21-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047342(n), n=1..100); # _Wesley Ivan Hurt_, Jun 13 2016
%t A047342 Select[Range[0,150], MemberQ[{0,3,4}, Mod[#,7]]&] (* _Harvey P. Dale_, Mar 18 2011 *)
%t A047342 CoefficientList[Series[(3x+x^2+3x^3)/((-1+x)^2(1+x+x^2)),{x,0,160}],x] (* _Vladimir Joseph Stephan Orlovsky_, Jan 26 2012 *)
%t A047342 LinearRecurrence[{1, 0, 1, -1},{0, 3, 4, 7},61] (* _Ray Chandler_, Aug 25 2015 *)
%o A047342 (Magma) [n : n in [0..150] | n mod 7 in [0, 3, 4]]; // _Wesley Ivan Hurt_, Jun 13 2016
%Y A047342 Cf. A168223, A168224.
%K A047342 nonn,easy
%O A047342 1,2
%A A047342 _N. J. A. Sloane_