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%I #20 Sep 08 2022 08:45:29
%S 0,0,-1,-1,2,2,-3,-3,4,4,-5,-5,6,6,-7,-7,8,8,-9,-9,10,10,-11,-11,12,
%T 12,-13,-13,14,14,-15,-15,16,16,-17,-17,18,18,-19,-19,20,20,-21,-21,
%U 22,22,-23,-23,24,24,-25,-25,26,26,-27,-27,28,28,-29,-29,30,30,-31,-31
%N Signed repeated natural numbers.
%C Hankel transform of A093387.
%H Vincenzo Librandi, <a href="/A127365/b127365.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,-2,0,-1)
%F G.f.: -x^2*(1+x)/(1+x^2)^2.
%F a(n) = floor(n/2)*(sin(n*Pi/2) + cos(n*Pi/2)).
%F a(n) = floor(n/2)*(-1)^floor(n/2) = A004526(n)*(-1)^A004526(n). - _Wesley Ivan Hurt_, Dec 10 2013
%p A127365:=n->floor(n/2)*(-1)^floor(n/2); seq(A127365(n), n=0..100); # _Wesley Ivan Hurt_, Nov 30 2013
%t With[{c=Table[n (-1)^n,{n,0,30}]},Riffle[c,c]] (* _Harvey P. Dale_, Jul 21 2013 *)
%t LinearRecurrence[{0, -2, 0, -1}, {0, 0, -1, -1}, 100] (* _Vincenzo Librandi_, Nov 18 2018 *)
%o (Magma) [(n div 2)*(-1)^(n div 2): n in [0..100]]; // _Vincenzo Librandi_, Nov 18 2018
%Y Cf. A004526.
%K easy,sign
%O 0,5
%A _Paul Barry_, Jan 11 2007
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