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%I #22 Mar 19 2024 15:32:02
%S 0,3,7,8,11,15,16,19,23,24,27,31,32,35,39,40,43,47,48,51,55,56,59,63,
%T 64,67,71,72,75,79,80,83,87,88,91,95,96,99,103,104,107,111,112,115,
%U 119,120,123,127,128,131,135,136,139,143,144,147,151,152,155,159
%N Numbers that are congruent to {0, 3, 7} mod 8.
%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*(x+3)*(1+x) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Jul 10 2015
%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) = 8*n/3-2+cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)).
%F a(3k) = 8k-1, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)
%p A047528:=n->8*n/3-2+cos(2*n*Pi/3)-sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047528(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016
%t Select[Range[0, 150], MemberQ[{0, 3, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 10 2016 *)
%t LinearRecurrence[{1,0,1,-1},{0,3,7,8},70] (* _Harvey P. Dale_, Jun 12 2019 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 3, 7]]; // _Wesley Ivan Hurt_, Jun 10 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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