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%I #22 Dec 25 2023 01:51:17
%S 3,2,1,0,5,4,9,8,7,6,11,10,15,14,13,12,17,16,21,20,19,18,23,22,27,26,
%T 25,24,29,28,33,32,31,30,35,34,39,38,37,36,41,40,45,44,43,42,47,46,51,
%U 50,49,48,53,52,57,56,55,54,59,58,63,62,61,60,65,64,69
%N Permutation of the nonnegative integers [6k+3, 6k+2, 6k+1, 6k, 6k+5, 6k+4].
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F a(n) = 1 + abs(n - 2 - 6*round((2n - 3)/6)) for n > 3.
%F G.f.: (3-x-x^2-x^3+5*x^4-x^5+2*x^6)/(1-x-x^6+x^7). - _Robert Israel_, Dec 13 2016
%F Sum_{n>=0, n!=3} (-1)^n/a(n) = log(2) (A002162). - _Amiram Eldar_, Dec 25 2023
%p f:= gfun:-rectoproc({a(n+7)-a(n+6)-a(n+1)+a(n)=0, seq(a(i)=[3, 2, 1, 0, 5, 4, 9][i+1],i=0..6)},a(n),remember):
%p map(f, [$0..100]); # _Robert Israel_, Dec 13 2016
%t Reverse/@TakeDrop[#,4]&/@Partition[Range[0,80],6]//Flatten (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[ {1,0,0,0,0,1,-1},{3,2,1,0,5,4,9},80] (* _Harvey P. Dale_, Dec 16 2017 *)
%o (Magma) &cat[[6*k+3, 6*k+2, 6*k+1, 6*k, 6*k+5, 6*k+4] : k in [0..20]];
%Y Cf. A002162, A263824.
%K nonn,easy
%O 0,1
%A _Wesley Ivan Hurt_, Dec 09 2016
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