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%I #33 Sep 08 2022 08:44:57
%S 0,1,2,8,9,10,16,17,18,24,25,26,32,33,34,40,41,42,48,49,50,56,57,58,
%T 64,65,66,72,73,74,80,81,82,88,89,90,96,97,98,104,105,106,112,113,114,
%U 120,121,122,128,129,130,136,137,138,144,145,146,152,153,154
%N Numbers that are congruent to {0, 1, 2} 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*(1 + x + 6*x^2)/((1 - x)*(1 - x^3)).
%F a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k) = 8*3^(k-1) for k>0. - _Philippe Deléham_, Oct 24 2011
%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-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 8k-6, a(3k-1) = 8k-7, a(3k-2) = 8k-8. (End)
%F a(n) = n + 5*floor((n-1)/3) - 1. - _Bruno Berselli_, Feb 06 2017
%p A047469:=n->(24*n-39-15*cos(2*n*Pi/3)+5*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047469(n), n=1..100); # _Wesley Ivan Hurt_, Jun 09 2016
%t Select[Range[0, 150], MemberQ[{0, 1, 2}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Jun 09 2016 *)
%o (PARI) a(n)=n+(n-1)\3*5-1
%o (Magma) [n : n in [0..150] | n mod 8 in [0..2]]; // _Wesley Ivan Hurt_, Jun 09 2016
%Y Cf. A030341.
%Y Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.
%K nonn,easy
%O 1,3
%A _N. J. A. Sloane_
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