%I #24 Sep 08 2022 08:44:57

%S 0,3,4,8,11,12,16,19,20,24,27,28,32,35,36,40,43,44,48,51,52,56,59,60,

%T 64,67,68,72,75,76,80,83,84,88,91,92,96,99,100,104,107,108,112,115,

%U 116,120,123,124,128,131,132,136,139,140,144,147,148,152,155,156

%N Numbers that are congruent to {0, 3, 4} mod 8.

%H Vincenzo Librandi, <a href="/A047458/b047458.txt">Table of n, a(n) for n = 1..1000</a>

%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+4*x^2)/((1-x)^2*(1+x+x^2)). [_Colin Barker_, May 13 2012]

%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)

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

%F a(n) = 8*n/3-3-cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)).

%F a(3k) = 8k-4, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)

%p A047458:=n->8*n/3-3-cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047458(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016

%t Select[Range[0, 150], MemberQ[{0, 3, 4}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)

%t LinearRecurrence[{1,0,1,-1},{0,3,4,8},90] (* _Harvey P. Dale_, May 31 2017 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 3, 4]]; // _Wesley Ivan Hurt_, Jun 09 2016

%Y Union of A008586 and A017101. - _Michel Marcus_, Jun 01 2017

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_