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

0,1

Comments

Row sums are A105595.

Links

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

Formula

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

Example

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;

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 *)

Crossrefs

Cf. A047999, A103447, A105595, A105596.

Sequence in context: A267272 A181656 A090971 * A091949 A039984 A153639

Adjacent sequences: A105591 A105592 A105593 * A105595 A105596 A105597

Keyword

easy,nonn,tabl

Author

Paul Barry, Apr 14 2005

Status

approved