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A056699 First differences are 2,1,-2,3 (repeated).

%I A056699 #59 Sep 08 2022 08:45:01
%S A056699 1,3,4,2,5,7,8,6,9,11,12,10,13,15,16,14,17,19,20,18,21,23,24,22,25,27,
%T A056699 28,26,29,31,32,30,33,35,36,34,37,39,40,38,41,43,44,42,45,47,48,46,49,
%U A056699 51,52,50,53,55,56,54,57,59,60,58,61,63,64,62,65,67,68,66
%N A056699 First differences are 2,1,-2,3 (repeated).
%C A056699 Second quadrisection of natural numbers shifted right two places. - _Ralf Stephan_, Jun 10 2005
%C A056699 A permutation of the natural numbers partitioned into quadruples [4k-3,4k-1,4k,4k-2] for k > 0. Partition the natural number sequence into quadruples starting with (1,2,3,4); swap the second and third elements, then swap the third and fourth elements; repeat for all quadruples. - _Guenther Schrack_, Oct 18 2017
%H A056699 David A. Corneth, <a href="/A056699/b056699.txt">Table of n, a(n) for n = 1..10000</a>
%H A056699 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%H A056699 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A056699 G.f.: x*(2*x^4 - 2*x^3 + x^2 + 2*x + 1)/((x-1)^2*(x+1)*(x^2+1)). - _Colin Barker_, Nov 08 2012
%F A056699 From _Guenther Schrack_, Oct 18 2017: (Start)
%F A056699 a(n) = a(n-4) + 4 for n > 4.
%F A056699 a(n) = n + periodic[0,1,1,-2].
%F A056699 a(n) = A092486(A067060(n) - 1) for n > 0.
%F A056699 a(n) = A292576(n) - 2*((-1)^floor(n/2)) for n > 0.
%F A056699 a(A116966(n-1)) = A263449(n-1) for n > 0.
%F A056699 A263449(a(n) - 1) = A116966(n-1) for n > 0.
%F A056699 a(n+2) - a(n) = (-1)^floor(n^2/4)*A132400(n+1) for n > 0.
%F A056699 a(n) = a(n-1) + a(n-4) - a(n-5) for n > 5. (End)
%F A056699 a(n) = A298364(n-1) + 1 for n > 1. - _Guenther Schrack_, Feb 04 2018
%t A056699 LinearRecurrence[{1,0,0,1,-1},{1,3,4,2,5},70] (* _Harvey P. Dale_, May 10 2014 *)
%t A056699 Table[Floor[(n - ((-1)^n + (-1)^(n (n - 1) / 2) (2 + (-1)^n)) / 2)], {n, 100}] (* _Vincenzo Librandi_, Feb 05 2018 *)
%o A056699 (MATLAB) a = [1 3 4 2];
%o A056699 max = 10000;  % Generation of a b-file
%o A056699 for n := 5:max
%o A056699    a(n) = a(n-4) + 4;
%o A056699 end;
%o A056699 % _Guenther Schrack_, Oct 18 2017
%o A056699 (PARI) for(n=1, 10000, print1(n - ((-1)^n + (-1)^(n*(n-1)/2)*(2+(-1)^n))/2, ", ")) \\ _Guenther Schrack_, Oct 18 2017
%o A056699 (Magma) [Floor((n - ((-1)^n + (-1)^(n*(n-1)/2)*(2+(-1)^n)) / 2)): n in [1..100]]; // _Vincenzo Librandi_, Feb 05 2018
%Y A056699 Inverse: A284307.
%Y A056699 Sequence of fixed points: A016813(n-1) for n > 0.
%Y A056699 Odd elements: A005408(n-1) for n > 0.
%Y A056699 Indices of odd elements: A042963(n) for n > 0.
%Y A056699 Even elements: 2*A103889(n) for n > 0.
%Y A056699 Indices of even elements: A014601(n) for n > 0.
%Y A056699 Cf. A067060, A092486, A116966, A132400, A292576, A263449, A042938 (bisection)
%K A056699 nonn,easy
%O A056699 1,2
%A A056699 Michael Knauth (knauth_jur(AT)yahoo.de), Nov 21 2003