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%I #32 Nov 28 2023 10:57:26
%S 0,3,2,1,4,7,6,5,8,11,10,9,12,15,14,13,16,19,18,17,20,23,22,21,24,27,
%T 26,25,28,31,30,29,32,35,34,33,36,39,38,37,40,43,42,41,44,47,46,45,48,
%U 51,50,49,52,55,54,53,56,59,58,57,60,63,62,61,64,67,66,65,68,71,70,69,72
%N Lodumo_4 of A102370 (sloping binary numbers).
%C A permutation of the nonnegative integers.
%C A092486 preceded by a zero. - _Philippe Deléham_, May 05 2009
%C Fixed points are the even numbers. - _Wesley Ivan Hurt_, Oct 16 2015
%H G. C. Greubel, <a href="/A159966/b159966.txt">Table of n, a(n) for n = 0..10000</a>
%H OEIS wiki, <a href="https://oeis.org/wiki/Lodumo_transform">Lodumo transform</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F a(n) = lod_4 (A102370(n)).
%F From _Wesley Ivan Hurt_, Oct 16 2015: (Start)
%F G.f.: (3*x-4*x^2+3*x^3)/((x-1)^2*(1+x^2)).
%F a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4), n>3.
%F a(n) = n-(1-(-1)^n)*(-1)^((2*n+1-(-1)^n)/4).
%F a(2n) = A005843(n); a(2n+1) = A166549(n).
%F a(n+1) - a(n) = A132429(n)*(-1)^n. (End)
%F Sum_{n>=1} (-1)^(n+1)/a(n) = log(2) (A002162). - _Amiram Eldar_, Nov 28 2023
%p A159966:=n->n-(1-(-1)^n)*(-1)^((2*n+1-(-1)^n)/4): seq(A159966(n), n=0..100); # _Wesley Ivan Hurt_, Oct 16 2015
%t Table[n - (1 - (-1)^n) (-1)^((2 n + 1 - (-1)^n)/4), {n, 0, 40}] (* or *) CoefficientList[Series[(3 x - 4 x^2 + 3 x^3)/((x - 1)^2 (1 + x^2)), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Oct 16 2015 *)
%t LinearRecurrence[{2,-2,2,-1},{0,3,2,1},80] (* _Harvey P. Dale_, Jul 02 2022 *)
%o (Magma) [n-(1-(-1)^n)*(-1)^((2*n+1-(-1)^n) div 4) : n in [0..100]]; // _Wesley Ivan Hurt_, Oct 16 2015
%o (PARI) concat(0, Vec((3*x-4*x^2+3*x^3)/((x-1)^2*(1+x^2)) + O(x^100))) \\ _Altug Alkan_, Oct 17 2015
%Y Cf. A002162, A005843, A102370, A132429, A158459, A166549.
%K easy,nonn,less,base
%O 0,2
%A _Philippe Deléham_, Apr 28 2009
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