A047347 - OEIS

%I #26 Sep 08 2022 08:44:57

%S 0,1,4,7,8,11,14,15,18,21,22,25,28,29,32,35,36,39,42,43,46,49,50,53,

%T 56,57,60,63,64,67,70,71,74,77,78,81,84,85,88,91,92,95,98,99,102,105,

%U 106,109,112,113,116,119,120,123,126,127,130,133,134,137,140,141

%N Numbers that are congruent to {0, 1, 4} 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*(1+3*x+3*x^2)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

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

%F a(n) = 7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)).

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

%p A047347:=n->7*n/3-3+4*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047347(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t Select[Range[0,200], MemberQ[{0,1,4}, Mod[#,7]]&] (* or *) LinearRecurrence[{1,0,1,-1}, {0,1,4,7}, 100] (* _Harvey P. Dale_, Dec 05 2012 *)

%o (Magma) [n : n in [0..150] | n mod 7 in [0, 1, 4]]; // _Wesley Ivan Hurt_, Jun 10 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_