A047321 - OEIS

%I #14 Sep 08 2022 08:44:56

%S 1,5,6,8,12,13,15,19,20,22,26,27,29,33,34,36,40,41,43,47,48,50,54,55,

%T 57,61,62,64,68,69,71,75,76,78,82,83,85,89,90,92,96,97,99,103,104,106,

%U 110,111,113,117,118,120,124,125,127,131,132,134,138,139,141

%N Numbers that are congruent to {1, 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*(1+4*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-6-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9.

%F a(3k) = 7k-1, a(3k-1) = 7k-2, a(3k-2) = 7k-6. (End)

%p A047321:=n->(21*n-6-3*cos(2*n*Pi/3)-5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047321(n), n=1..100); # _Wesley Ivan Hurt_, Jun 07 2016

%t Select[Range[0, 150], MemberQ[{1, 5, 6}, Mod[#, 7]] &] (* _Wesley Ivan Hurt_, Jun 07 2016 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [1, 5, 6]]; // _Wesley Ivan Hurt_, Jun 07 2016

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_