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%I #12 Sep 08 2022 08:44:57
%S 3,4,5,11,12,13,19,20,21,27,28,29,35,36,37,43,44,45,51,52,53,59,60,61,
%T 67,68,69,75,76,77,83,84,85,91,92,93,99,100,101,107,108,109,115,116,
%U 117,123,124,125,131,132,133,139,140,141,147,148,149,155,156,157
%N Numbers that are congruent to {3, 4, 5} mod 8.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F From _Wesley Ivan Hurt_, Jun 09 2016: (Start)
%F G.f.: x*(3+x+x^2+3*x^3)/((x-1)^2*(1+x+x^2)).
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (24*n-12-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-3, a(3k-1) = 8k-4, a(3k-2) = 8k-5. (End)
%p A047598:=n->(24*n-12-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047598(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t Select[Range[0, 150], MemberQ[{3, 4, 5}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%t LinearRecurrence[{1,0,1,-1},{3,4,5,11},80] (* _Harvey P. Dale_, May 20 2021 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [3..5]]; // _Wesley Ivan Hurt_, Jun 09 2016
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
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