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A047231 Numbers that are congruent to {0, 3, 4} mod 6.

%I A047231 #26 Sep 08 2022 08:44:56
%S A047231 0,3,4,6,9,10,12,15,16,18,21,22,24,27,28,30,33,34,36,39,40,42,45,46,
%T A047231 48,51,52,54,57,58,60,63,64,66,69,70,72,75,76,78,81,82,84,87,88,90,93,
%U A047231 94,96,99,100,102,105,106,108,111,112,114,117,118,120,123,124
%N A047231 Numbers that are congruent to {0, 3, 4} mod 6.
%H A047231 Vincenzo Librandi, <a href="/A047231/b047231.txt">Table of n, a(n) for n = 1..1000</a>
%H A047231 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A047231 From _R. J. Mathar_, Aug 05 2010: (Start)
%F A047231 G.f.: x^2*(3+x+2*x^2) / ( (1+x+x^2)*(x-1)^2 ).
%F A047231 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
%F A047231 a(n) = 2*n+2-(11+A061347(n+1))/3. (End)
%F A047231 From _Wesley Ivan Hurt_, Jun 13 2016: (Start)
%F A047231 a(n) = (6*n-5-cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/3.
%F A047231 a(3k) = 6k-2, a(3k-1) = 6k-3, a(3k-2) = 6k-6. (End)
%F A047231 Sum_{n>=2} (-1)^n/a(n) = log(2)/3 + (1-2/sqrt(3))*Pi/12. - _Amiram Eldar_, Dec 14 2021
%p A047231 A047231:=n->(6*n-5-cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/3: seq(A047231(n), n=1..100); # _Wesley Ivan Hurt_, Jun 13 2016
%t A047231 Select[Range[0, 600], MemberQ[{0, 3, 4}, Mod[#, 6]]&] (* _Vincenzo Librandi_, Jan 06 2013 *)
%t A047231 LinearRecurrence[{1,0,1,-1},{0,3,4,6},70] (* _Harvey P. Dale_, Sep 03 2017 *)
%o A047231 (Magma) [n: n in [0..120] | n mod 6 in [0, 3, 4]]; // _Vincenzo Librandi_, Jan 06 2013
%Y A047231 Cf. A061347.
%K A047231 nonn,easy
%O A047231 1,2
%A A047231 _N. J. A. Sloane_