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%I #14 Sep 08 2022 08:44:57
%S 4,5,7,12,13,15,20,21,23,28,29,31,36,37,39,44,45,47,52,53,55,60,61,63,
%T 68,69,71,76,77,79,84,85,87,92,93,95,100,101,103,108,109,111,116,117,
%U 119,124,125,127,132,133,135,140,141,143,148,149,151,156,157
%N Numbers that are congruent to {4, 5, 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*(4+x+2*x^2+x^3)/((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Nov 06 2015
%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) = (24*n-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-1, a(3k-1) = 8k-3, a(3k-2) = 8k-4. (End)
%p A047491:=n->(24*n-9*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047491(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t Select[Range[0, 150], MemberQ[{4, 5, 7}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%t LinearRecurrence[{1,0,1,-1},{4,5,7,12},60] (* _Harvey P. Dale_, Feb 06 2019 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [4, 5, 7]]; // _Wesley Ivan Hurt_, Jun 09 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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