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%I #24 Sep 08 2022 08:44:56
%S 0,2,5,6,8,11,12,14,17,18,20,23,24,26,29,30,32,35,36,38,41,42,44,47,
%T 48,50,53,54,56,59,60,62,65,66,68,71,72,74,77,78,80,83,84,86,89,90,92,
%U 95,96,98,101,102,104,107,108,110,113,114,116,119,120,122,125
%N Numbers that are congruent to {0, 2, 5} mod 6.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F a(n) = 3*n-3*floor(n/3)-(n^2 mod 3), with offset 0. - _Gary Detlefs_, Mar 19 2010
%F G.f.: x^2*(x+2)*(1+x) / ((1+x+x^2)*(x-1)^2). - _R. J. Mathar_, Oct 08 2011
%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) = (6*n-5+2*cos(2*n*Pi/3))/3.
%F a(3k) = 6k-1, a(3k-1) = 6k-4, a(3k-2) = 6k-6. (End)
%F E.g.f.: (3 + (6*x - 5)*exp(x) + 2*cos(sqrt(3)*x/2)*(cosh(x/2) - sinh(x/2)))/3. - _Ilya Gutkovskiy_, Jun 14 2016
%F Sum_{n>=2} (-1)^n/a(n) = log(2)/3 + log(2+sqrt(3))/(2*sqrt(3)) - (3-sqrt(3))*Pi/18. - _Amiram Eldar_, Dec 14 2021
%p seq(3*n-3*floor(n/3)-(n^2 mod 3), n=0..54); # _Gary Detlefs_, Mar 19 2010
%t Select[Range[0,110], MemberQ[{0,2,5}, Mod[#,6]]&] (* or *) LinearRecurrence[{1,0,1,-1}, {0,2,5,6}, 60] (* _Harvey P. Dale_, Aug 31 2015 *)
%o (Magma) [n : n in [0..150] | n mod 6 in [0, 2, 5]]; // _Wesley Ivan Hurt_, Jun 13 2016
%Y Cf. A011655. [_Gary Detlefs_, Mar 19 2010]
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
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