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%I #50 Sep 08 2022 08:46:09
%S 0,1,2,4,8,3,6,12,16,5,10,20,24,7,14,28,32,9,18,36,40,11,22,44,48,13,
%T 26,52,56,15,30,60,64,17,34,68,72,19,38,76,80,21,42,84,88,23,46,92,96,
%U 25,50,100,104,27,54,108,112,29,58,116,120
%N A permutation of the nonnegative numbers: a(4n) = 8n, a(4n+1) = 2n + 1, a(4n+2) = 4n + 2, a(4n+3) = 8n + 4.
%C A permutation of the nonnegative integers.
%H G. C. Greubel, <a href="/A247555/b247555.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F a(n) = a(n-4) + a(n-8) - a(n-12).
%F a(n) = 2*a(n-4) - a(n-8). - _Colin Barker_, Sep 19 2014
%F G.f.: x*(4*x^6 + 2*x^5 + x^4 + 8*x^3 + 4*x^2 + 2*x + 1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - _Colin Barker_, Sep 19 2014
%F a(n) = (11*n-3+(n+3)*(-1)^n+(4*n-1+(-1)^n)*cos(n*Pi/2)+2*(9-3*n+4(-1)^n)* sin(n*Pi/2))/8. - _Wesley Ivan Hurt_, May 07 2021
%t a[n_]:=Switch[Mod[n,4],0,2 n,1,(n+1)/2,2,n,3,2 n-2]; Table[a[n],{n,0,60}] (* _Jean-François Alcover_, Oct 09 2014 *)
%t LinearRecurrence[{0,0,0,2,0,0,0,-1}, {0,1,2,4,8,3,6,12}, 50] (* _G. C. Greubel_, May 01 2018 *)
%o (PARI) Vec(x*(4*x^6+2*x^5+x^4+8*x^3+4*x^2+2*x+1)/((x-1)^2*(x+1)^2*(x^2+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 19 2014
%o (Magma) &cat[[4*(i-1),i,2*i,4*i]: i in [1..50 by 2]]; // _Bruno Berselli_, Sep 19 2014
%Y Cf. A005408, A008590, A016825, A017113, A225055, A001477, A111284.
%K nonn,easy,less
%O 0,3
%A _Paul Curtz_, Sep 19 2014