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%I #25 Mar 31 2023 05:13:47
%S 0,3,5,8,11,13,16,19,21,24,27,29,32,35,37,40,43,45,48,51,53,56,59,61,
%T 64,67,69,72,75,77,80,83,85,88,91,93,96,99,101,104,107,109,112,115,
%U 117,120,123,125,128,131,133,136,139,141,144,147,149,152,155,157
%N Numbers that are congruent to {0, 3, 5} mod 8.
%H Vincenzo Librandi, <a href="/A047622/b047622.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 From _R. J. Mathar_, Oct 18 2008: (Start)
%F G.f.: x^2*(3+2*x+3*x^2)/((1-x)^2*(1+x+x^2)).
%F a(n) = A008576(n-1), for n>1. (End)
%F a(n) = floor((8n-7)/3). - _Gary Detlefs_, Mar 07 2010
%F From _Wesley Ivan Hurt_, Jun 13 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (24*n-24-3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-3, a(3k-1) = 8k-5, a(3k-2) = 8k-8. (End)
%F a(n) = A047408(n) - 1. - _Lorenzo Sauras Altuzarra_, Jan 31 2023
%F E.g.f.: 3 + (8/3)*exp(x)*(x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2))/9. - _Stefano Spezia_, Mar 30 2023
%p seq(floor((8*n-7)/3), n=1..52); # _Gary Detlefs_, Mar 07 2010
%t Select[Range[0,150], MemberQ[{0,3,5}, Mod[#,8]]&] (* _Harvey P. Dale_, Oct 04 2012 *)
%t LinearRecurrence[{1, 0, 1, -1}, {0, 3, 5, 8}, 100] (* _Vincenzo Librandi_, Jun 14 2016 *)
%o (Magma) [n : n in [0..150] | n mod 8 in [0, 3, 5]]; // _Wesley Ivan Hurt_, Jun 13 2016
%Y Cf. A008576, A047408.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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