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A105594 Triangle read by rows: abs(A103447)*A047999 mod 2.

%I A105594 #21 Jan 15 2020 07:45:09
%S A105594 1,0,1,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,1,1,0,0,0,0,0,0,
%T A105594 0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,1,1,0,0,
%U A105594 0,1,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,1,0,1,0,0,1,1,0,0,1,1,0,1,0,1
%N A105594 Triangle read by rows: abs(A103447)*A047999 mod 2.
%C A105594 Row sums are A105595.
%H A105594 Robert Israel, <a href="/A105594/b105594.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)
%F A105594 T(n, k) = mod(Sum_{j=0..n}(abs(mu(binomial(n,j)))*mod(binomial(j,k),2)), 2).
%e A105594 Triangle starts
%e A105594 1;
%e A105594 0,1;
%e A105594 1,1,1;
%e A105594 0,0,0,1;
%e A105594 1,0,1,0,1;
%e A105594 0,1,0,1,0,1;
%e A105594 0,0,0,0,1,1,1;
%p A105594 A105594 := proc(n,k)
%p A105594     add( abs(numtheory[mobius](binomial(n,j)))*modp(binomial(j,k),2) ,j=0..n) ;
%p A105594     % mod 2 ;
%p A105594 end proc: # _R. J. Mathar_, Nov 28 2014
%t A105594 T[n_, k_] := Sum[Abs[MoebiusMu[Binomial[n, j]]*Mod[Binomial[j, k], 2]], {j, 0, n}] // Mod[#, 2]&;
%t A105594 Table[T[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jan 15 2020 *)
%Y A105594 Cf. A047999, A103447, A105595, A105596.
%K A105594 easy,nonn,tabl
%O A105594 0,1
%A A105594 _Paul Barry_, Apr 14 2005