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%I #28 Sep 08 2022 08:44:56
%S 0,3,4,5,8,9,10,13,14,15,18,19,20,23,24,25,28,29,30,33,34,35,38,39,40,
%T 43,44,45,48,49,50,53,54,55,58,59,60,63,64,65,68,69,70,73,74,75,78,79,
%U 80,83,84,85,88,89,90,93,94,95,98,99,100,103,104,105,108
%N Numbers that are congruent to {0, 3, 4} mod 5.
%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*(3+x+x^2) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Oct 08 2011
%F From _Wesley Ivan Hurt_, Jun 14 2016: (Start)
%F a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F a(n) = (15*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9.
%F a(3k) = 5k-1, a(3k-1) = 5k-2, a(3k-2) = 5k-5. (End)
%F Sum_{n>=2} (-1)^n/a(n) = 3*log(2)/5 - sqrt(1-2/sqrt(5))*Pi/5. - _Amiram Eldar_, Jan 01 2022
%p A047205:=n->(15*n-9-4*sqrt(3)*sin(2*n*Pi/3))/9: seq(A047205(n), n=1..100); # _Wesley Ivan Hurt_, Jun 14 2016
%t Select[Range[0, 200], MemberQ[{0, 3, 4}, Mod[#, 5]] &] (* _Vladimir Joseph Stephan Orlovsky_, Feb 12 2012 *)
%o (Magma) [ n : n in [0..150] | n mod 5 in [0, 3, 4] ]; // _Vincenzo Librandi_, Mar 31 2011
%o (PARI) a(n)=n\3*5+[-1,0,3][n%3+1] \\ _Charles R Greathouse IV_, Dec 22 2011
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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