A114000 Triangle read by rows: column k has g.f. = Sum_{k>0} x^k/(1-x^(2*k+1)).

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

Offset: 0

Author

Paul Barry, Nov 12 2005

Keywords

• easy
• nonn
• tabl

Comments

Number triangle related to divisors of 2n+1. Row n has a 1 in column k iff 2*k+1 divides 2*n+1. - N. J. A. Sloane, Dec 23 2020

Examples

			Triangle begins
1
1, 1,
1, 0, 1,
1, 0, 0, 1,
1, 1, 0, 0, 1,
1, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 1,
1, 1, 1, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1
...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..11324 (rows 0..150 of the triangle, flattened).

Crossrefs

Cf. A001227, A082647, A131576.

Rows sums are A099774. Rows as decimals give A114001.

Programs

Mathematica

A114000row[n_]:=Boole[Divisible[2n+1,2Range[0,n]+1]];
Array[A114000row,20,0] (* Paolo Xausa, Dec 04 2023 *)

Extensions

Edited by N. J. A. Sloane, Dec 23 2020