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A249693 a(4n) = 3*n+1, a(2n+1) = 3*n+2, a(4n+2) = 3*n.

%I A249693 #48 Sep 08 2022 08:46:10
%S A249693 1,2,0,5,4,8,3,11,7,14,6,17,10,20,9,23,13,26,12,29,16,32,15,35,19,38,
%T A249693 18,41,22,44,21,47,25,50,24,53,28,56,27,59,31,62,30,65,34,68,33,71,37,
%U A249693 74,36,77,40,80,39,83,43,86,42,89,46,92,45
%N A249693 a(4n) = 3*n+1, a(2n+1) = 3*n+2, a(4n+2) = 3*n.
%C A249693 A permutation of the nonnegative numbers.
%H A249693 G. C. Greubel, <a href="/A249693/b249693.txt">Table of n, a(n) for n = 0..5000</a>
%H A249693 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,-1).
%F A249693 a(n+4) = a(n) + (sequence of period 2: repeat 3, 6).
%F A249693 a(4n+1) = 2*a(4n).
%F A249693 a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).
%F A249693 a(n) is the rank of A061037(n) = -1, -3, 0, 5, ... in A247829(n) = 0, -1, -3, 2, ... .
%F A249693 G.f.: (1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6).
%F A249693 a(n) = (1 + 9*n - 3*(n+1)*(-1)^n + 10*cos(n*Pi/2))/8. - _Robert Israel_, Dec 03 2014
%t A249693 a[n_] := (1/8)*(3*(-1)^(n+1)*(n+1)+9*n+10*{1, 0, -1, 0}[[Mod[n, 4]+1]]+1); Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Dec 04 2014, after _Robert Israel_ *)
%o A249693 (PARI) x='x+O('x^75); Vec((1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6)) \\ _G. C. Greubel_, Sep 20 2018
%o A249693 (Magma) m:=75; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 + 2*x - x^2 + 3*x^3 + 3*x^4 + x^5)/(1 - x^2 - x^4 + x^6))); // _G. C. Greubel_, Sep 20 2018
%Y A249693 Cf. A001477, A010704, A010857, A016789, A061037.
%K A249693 nonn
%O A249693 0,2
%A A249693 _Paul Curtz_, Dec 03 2014