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%I #25 Sep 08 2022 08:46:16
%S 3,2,1,4,5,6,9,8,7,10,11,12,15,14,13,16,17,18,21,20,19,22,23,24,27,26,
%T 25,28,29,30,33,32,31,34,35,36,39,38,37,40,41,42,45,44,43,46,47,48,51,
%U 50,49,52,53,54,57,56,55,58,59,60,63,62,61,64,65,66,69,68,67,70,71,72,75,74,73
%N Expansion of (3 - 4*x + 3*x^2 + x^4)/((1 - x)^2*(1 + x^2 + x^4)).
%C Permutation of the positive integers, with 6k+1 and 6k+3 swapped for every k.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-2,2,-1).
%F G.f.: (3 - 4*x + 3*x^2 + x^4)/((1 - x)^2*(1 + x^2 + x^4)).
%F a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6).
%F a(n) = 3 - n + 4*floor(n/6) + 2*floor((n+1)/6) + 2*floor((n+2)/6) + 4*floor((n+3)/6). - _Vaclav Kotesovec_, Apr 19 2016
%p A271830:=n->3-n+4*floor(n/6)+2*floor((n+1)/6)+2*floor((n+2)/6)+4*floor((n+3)/6): seq(A271830(n), n=0..150); # _Wesley Ivan Hurt_, Apr 20 2016
%t CoefficientList[Series[(3 - 4 x + 3 x^2 + x^4)/((1 - x)^2 (1 + x^2 + x^4)), {x, 0, 75}], x]
%t LinearRecurrence[{2, -2, 2, -2, 2, -1}, {3, 2, 1, 4, 5, 6}, 75]
%o (PARI) x='x+O('x^99); Vec((3-4*x+3*x^2+x^4)/((1-x)^2*(1+x^2+x^4))) \\ _Altug Alkan_, Apr 18 2016
%o (Magma) [3 - n + 4*Floor(n/6) + 2*Floor((n+1)/6) + 2*Floor((n+2)/6) + 4*Floor((n+3)/6) : n in [0..100]]; // _Wesley Ivan Hurt_, Apr 20 2016
%Y Cf. A000027, A080412.
%K nonn,easy
%O 0,1
%A _Ilya Gutkovskiy_, Apr 18 2016
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