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A047378 Numbers that are congruent to {2, 4, 5} mod 7.

%I A047378 #17 Sep 08 2022 08:44:57
%S A047378 2,4,5,9,11,12,16,18,19,23,25,26,30,32,33,37,39,40,44,46,47,51,53,54,
%T A047378 58,60,61,65,67,68,72,74,75,79,81,82,86,88,89,93,95,96,100,102,103,
%U A047378 107,109,110,114,116,117,121,123,124,128,130,131,135,137,138,142
%N A047378 Numbers that are congruent to {2, 4, 5} mod 7.
%H A047378 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047378 G.f.: x*(2+2*x+x^2+2*x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 04 2011
%F A047378 From _Wesley Ivan Hurt_, Jun 09 2016: (Start)
%F A047378 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047378 a(n) = (21*n-9-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
%F A047378 a(3k) = 7k-2, a(3k-1) = 7k-3, a(3k-2) = 7k-5. (End)
%p A047378 A047378:=n->(21*n-9-9*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047378(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t A047378 Select[Range[0, 150], MemberQ[{2, 4, 5}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%t A047378 LinearRecurrence[{1,0,1,-1},{2,4,5,9},100] (* _Harvey P. Dale_, Jul 14 2022 *)
%o A047378 (Magma) [n : n in [0..150] | n mod 7 in [2, 4, 5]]; // _Wesley Ivan Hurt_, Jun 09 2016
%Y A047378 Cf. A153727 (first differences).
%K A047378 nonn,easy
%O A047378 1,1
%A A047378 _N. J. A. Sloane_