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

0,1

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

Links

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

Example

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
...

Mathematica

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

Crossrefs

Cf. A001227, A082647, A131576.

Rows sums are A099774. Rows as decimals give A114001.

Sequence in context: A158856 A154957 A140865 * A131218 A174391 A343910

Adjacent sequences: A113997 A113998 A113999 * A114001 A114002 A114003

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 12 2005

Extensions

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

Status

approved