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Triangle T(n,k) read by rows. Signed subsequence of A051731.
4

%I #5 Apr 25 2016 11:44:15

%S -1,1,0,1,0,0,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0,1,0,0,0,0,0,0,1,1,0,1,0,0,

%T 0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,

%U 1,1,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,1,0,0,0,0,0,0,0

%N Triangle T(n,k) read by rows. Signed subsequence of A051731.

%C Let A=A176890*A176890, B=A*A, C=B*B, D=C*C and so on, then the leftmost column in the last matrix converges to the Moebius function A008683.

%F T(n,k) = if n=1 and k=1 then -1 elseif n=k then 0 elseif k divides n then 1 else 0.

%e Table begins:

%e -1,

%e 1,0,

%e 1,0,0,

%e 1,1,0,0,

%e 1,0,0,0,0,

%e 1,1,1,0,0,0,

%e 1,0,0,0,0,0,0,

%e 1,1,0,1,0,0,0,0,

%e 1,0,1,0,0,0,0,0,0,

%e 1,1,0,0,1,0,0,0,0,0,

%o (Excel) =if(and(row()=1;column()=1);-1;if(mod(row();column())=0;1;0)-if(and(column()>1;row()=column());1;0))

%Y Cf. A051731, A008683.

%Y This is A176918 * the diagonalized mu(n).

%K sign,tabl

%O 1,1

%A Mats Granvik and _Gary W. Adamson_, Apr 28 2010