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A195084 a(2n-1) = 2-n, a(2n) = 2+n.

%I A195084 #53 Sep 22 2024 22:22:08
%S A195084 2,1,3,0,4,-1,5,-2,6,-3,7,-4,8,-5,9,-6,10,-7,11,-8,12,-9,13,-10,14,
%T A195084 -11,15,-12,16,-13,17,-14,18,-15,19,-16,20,-17,21,-18,22,-19,23,-20,
%U A195084 24,-21,25,-22,26,-23,27,-24,28,-25,29,-26,30,-27,31,-28,32,-29,33
%N A195084 a(2n-1) = 2-n, a(2n) = 2+n.
%C A195084 Start with a(0)=2, subtract 1, add 2, subtract 3, add 4, subtract 5 and so on.
%C A195084 A permutation of all integers. - _Ruud H.G. van Tol_, Sep 21 2024
%H A195084 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the integers</a>
%H A195084 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,1).
%F A195084 From _Bruno Berselli_, Sep 12 2011: (Start)
%F A195084 G.f.: (2*x^2+3*x+2)/((1-x)*(1+x)^2).
%F A195084 a(n) = a(-n-1) = -((2*n+1)*a(n-1)-7*n)/(2*n-1) = -a(n-1)+a(n-2)+a(n-3).
%F A195084 a(n) = ((2*n+1)*(-1)^n+7)/4.
%F A195084 a(n) = 2 - A001057(n).
%F A195084 a(n)-a(n-1) = A038608(n); a(n)+a(n-1) = A010702(n-1).
%F A195084 Sum(n=1..n, a(i)) = ((n+1)*(-1)^n+7*n-1)/4, i.e. A016777 and A008586 (>0) alternately. (End)
%F A195084 a(n+2) = a(n) + (-1)^n. - _Vincenzo Librandi_, Sep 12 2011
%F A195084 E.g.f.: ((4 - x)*cosh(x) + (3 + x)*sinh(x))/2. - _Stefano Spezia_, Sep 22 2024
%Y A195084 Cf. A001057, A168230.
%K A195084 sign,easy
%O A195084 0,1
%A A195084 _Dave Durgin_, Sep 08 2011
%E A195084 Definition corrected by _Omar E. Pol_, Sep 11 2011
%E A195084 a(0)=2 prepended by _Ruud H.G. van Tol_, Sep 21 2024