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

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, 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, 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

Offset: 0

Author

Paul Barry, Apr 14 2005

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A105595.

Examples

			Triangle starts
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;
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)

Crossrefs

Cf. A047999, A103447, A105595, A105596.

Programs

Maple

A105594 := proc(n,k)
    add( abs(numtheory[mobius](binomial(n,j)))*modp(binomial(j,k),2) ,j=0..n) ;
    % mod 2 ;
end proc: # R. J. Mathar, Nov 28 2014

Mathematica

T[n_, k_] := Sum[Abs[MoebiusMu[Binomial[n, j]]*Mod[Binomial[j, k], 2]], {j, 0, n}] // Mod[#, 2]&;
Table[T[n, k], {n, 0, 13}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 15 2020 *)

Formula

T(n, k) = mod(Sum_{j=0..n}(abs(mu(binomial(n,j)))*mod(binomial(j,k),2)), 2).