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a(0)=0; thereafter (-1)^(n+1)*n appears n times.
2

%I #22 Nov 05 2024 12:19:03

%S 0,1,-2,-2,3,3,3,-4,-4,-4,-4,5,5,5,5,5,-6,-6,-6,-6,-6,-6,7,7,7,7,7,7,

%T 7,-8,-8,-8,-8,-8,-8,-8,-8,9,9,9,9,9,9,9,9,9,-10,-10,-10,-10,-10,-10,

%U -10,-10,-10,-10,11,11,11,11,11,11,11,11,11,11,11,-12,-12,-12,-12,-12,-12,-12,-12,-12,-12

%N a(0)=0; thereafter (-1)^(n+1)*n appears n times.

%H Chai Wah Wu, <a href="/A274094/b274094.txt">Table of n, a(n) for n = 0..10011</a>

%p s1:=[0];

%p for n from 1 to 15 do

%p for i from 1 to n do

%p s1:=[op(s1),(-1)^(n+1)*n]; od: od:

%p s1;

%t Join[{0}, Flatten[Table[(-1)^(n+1)*n, {n, 15}, {n}]]] (* _Paolo Xausa_, Sep 30 2024 *)

%o (Python)

%o A274094_list = [0]+ [i for n in range(1,142) for i in [n if n % 2 else -n]*n] # _Chai Wah Wu_, Jun 11 2016

%o (Python)

%o from math import isqrt

%o def A274094(n): return m if (m:=isqrt(n<<3)+1>>1)&1 else -m # _Chai Wah Wu_, Nov 05 2024

%Y Cf. A002024, A274093.

%Y Partial sums of A010816.

%K sign

%O 0,3

%A _N. J. A. Sloane_, Jun 10 2016