A127365 - OEIS

%I #23 Jul 14 2024 17:41:59

%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

%F E.g.f.: (x*cos(x) - (1 + x)*sin(x))/2. - _Stefano Spezia_, Jul 14 2024

%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, A093387.

%K easy,sign

%O 0,5

%A _Paul Barry_, Jan 11 2007