|
%I #16 Sep 08 2022 08:44:56
%S 1,2,6,8,9,13,15,16,20,22,23,27,29,30,34,36,37,41,43,44,48,50,51,55,
%T 57,58,62,64,65,69,71,72,76,78,79,83,85,86,90,92,93,97,99,100,104,106,
%U 107,111,113,114,118,120,121,125,127,128,132,134,135,139,141
%N Numbers that are congruent to {1, 2, 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*(1+x+4*x^2+x^3) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 25 2011
%F From _Wesley Ivan Hurt_, Jun 07 2016: (Start)
%F a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
%F a(n) = (21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 7k-1, a(3k-1) = 7k-5, a(3k-2) = 7k-6. (End)
%p A047278:=n->(21*n-15+6*cos(2*n*Pi/3)+4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047278(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016
%t Table[(21*n-15+6*Cos[2*n*Pi/3]+4*Sqrt[3]*Sin[2*n*Pi/3])/9, {n,
%t 80}] (* _Wesley Ivan Hurt_, Jun 07 2016 *)
%t Select[Range[200],MemberQ[{1,2,6},Mod[#,7]]&] (* or *) LinearRecurrence[ {1,0,1,-1},{1,2,6,8},100] (* _Harvey P. Dale_, Dec 16 2018 *)
%o (Magma) [n : n in [1..150] | n mod 7 in [1, 2, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
|
