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%I #15 Nov 14 2023 08:33:12
%S 0,2,1,4,6,3,8,10,5,12,14,7,16,18,9,20,22,11,24,26,13,28,30,15,32,34,
%T 17,36,38,19,40,42,21,44,46,23,48,50,25,52,54,27,56,58,29,60,62,31,64,
%U 66,33,68,70,35,72,74,37,76,78,39,80,82,41,84,86,43,88,90,45,92,94,47
%N Inverse of A342131.
%C Permutation of the nonnegative numbers.
%H Paolo Xausa, <a href="/A367286/b367286.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2,0,0,-1).
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%F a(3*n) = 4*n, a(3*n+1) = 4*n+2, a(3*n+2) = 2*n+1.
%F a(n) = 2*a(n-3) - a(n-6) for n >= 6.
%F a(n) = A006369(n+1) - 1.
%F G.f.: x*(2+x+4*x^2+2*x^3+x^4)/(1-x^3)^2.
%F E.g.f.: exp(-x/2)*(exp(3*x/2)*(10*x + 1) + (2*x - 1)*cos(sqrt(3)*x/2) + sqrt(3)*(3 - 2*x)*sin(sqrt(3)*x/2))/9. - _Stefano Spezia_, Nov 12 2023
%t LinearRecurrence[{0,0,2,0,0,-1},{0,2,1,4,6,3},100] (* _Paolo Xausa_, Nov 14 2023 *)
%Y Cf. A006369, A342131.
%K nonn,easy
%O 0,2
%A _Philippe Deléham_, Nov 12 2023