A105586 A Moebius-binomial triangle.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,1

Comments

n-th row is all 1's unless n is not squarefree (see A013929). Row sums are A105587. Diagonal sums are A105588. Inverse is A105589.

Links

Table of n, a(n) for n=0..104.

Formula

Number triangle T(n, k)=if(k<=n, binomial(abs(mu(n)), abs(mu(k))), 0)

Example

Triangle starts
1;
1,1;
1,1,1;
1,1,1,1;
0,0,0,0,1;
1,1,1,1,1,1;
1,1,1,1,1,1,1;
1,1,1,1,1,1,1,1;
0,0,0,0,1,0,0,0,1;

Crossrefs

Sequence in context: A336546 A209929 A336556 * A202022 A136522 A352871

Adjacent sequences: A105583 A105584 A105585 * A105587 A105588 A105589

Keyword

easy,nonn,tabl

Author

Paul Barry, Apr 14 2005

Status

approved