%I #16 Sep 08 2022 08:44:56

%S 2,5,6,9,12,13,16,19,20,23,26,27,30,33,34,37,40,41,44,47,48,51,54,55,

%T 58,61,62,65,68,69,72,75,76,79,82,83,86,89,90,93,96,97,100,103,104,

%U 107,110,111,114,117,118,121,124,125,128,131,132,135,138,139,142

%N Numbers that are congruent to {2, 5, 6} mod 7.

%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*(2+3*x+x^2+x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Dec 03 2011

%F From _Wesley Ivan Hurt_, Jun 07 2016: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

%F a(n) = (21*n-3-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 7k-1, a(3k-1) = 7k-2, a(3k-2) = 7k-5. (End)

%p A047323:=n->(21*n-3-6*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047323(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016

%t Select[Range[0, 150], MemberQ[{2, 5, 6}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 07 2016 *)

%t LinearRecurrence[{1,0,1,-1},{2,5,6,9},70] (* _Harvey P. Dale_, Aug 29 2017 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [2, 5, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_