A279733 Triangle read by rows which is constructed with the diagram of the triangle of A237048 and filling the empty cells with zeros.

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

Offset

1

Comments

For the construction of this triangle we start with the right triangle of A237048 as shown below:

Row _

1 _|1|

2 _|1 _|

3 _|1 |1|

4 _|1 _|0|

5 _|1 |1 _|

6 _|1 _|0|1|

7 _|1 |1 |0|

8 _|1 _|0 _|0|

9 _|1 |1 |1 _|

10 _|1 _|0 |0|1|

11 _|1 |1 _|0|0|

12 _|1 _|0 |1 |0|

13 _|1 |1 |0 _|0|

14 _|1 _|0 _|0|1 _|

15 _|1 |1 |1 |0|1|

16 |1 |0 |0 |0|0|

...

And then filling with zeros the empty cells of the structure, as shown below:

Illustration of initial terms as a right triangle:

Row _

1 _|1|

2 _|1 0|

3 _|1 0 1|

4 _|1 0 0 0|

5 _|1 0 0 1 0|

6 _|1 0 0 0 0 1|

7 _|1 0 0 0 1 0 0|

8 _|1 0 0 0 0 0 0 0|

9 _|1 0 0 0 0 1 0 1 0|

10 _|1 0 0 0 0 0 0 0 0 1|

11 _|1 0 0 0 0 0 1 0 0 0 0|

12 _|1 0 0 0 0 0 0 0 0 1 0 0|

13 _|1 0 0 0 0 0 0 1 0 0 0 0 0|

14 _|1 0 0 0 0 0 0 0 0 0 0 0 1 0|

15 _|1 0 0 0 0 0 0 0 1 0 0 1 0 0 1|

16 |1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0|

...

Note that both triangles are related to the left hand part of the front view of the pyramid described A245092.

The position of the 1's are associated to the position of the subparts in the symmetric representation of sigma. For more information see A279391.

For more information about the pyramid and the symmetric representation of sigma see A237593.

For an isosceles triangle which arises from this triangle and its mirror see A275601.

Links

Table of n, a(n) for n=1..105.

Example

Triangle begins:
1;
1, 0;
1, 0, 1;
1, 0, 0, 0;
1, 0, 0, 1, 0;
1, 0, 0, 0, 0, 1;
1, 0, 0, 0, 1, 0, 0;
1, 0, 0, 0, 0, 0, 0, 0;
1, 0, 0, 0, 0, 1, 0, 1, 0;
1, 0, 0, 0, 0, 0, 0, 0, 0, 1;
...

Crossrefs

Row sums give A001227.

Cf. A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A239657, A245092, A249351, A261699, A262611, A262626, A275601, A279387, A279391, A279693, A281010, A281011.

Sequence in context: A104120 A254634 A108336 * A176723 A189126 A118268

Adjacent sequences: A279730 A279731 A279732 * A279734 A279735 A279736

Keyword

nonn,tabl

Author

Omar E. Pol, Dec 18 2016

Status

approved