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A279733
Triangle read by rows which is constructed with the diagram of the triangle of A237048 and filling the empty cells with zeros.
3
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.
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;
...
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Dec 18 2016
STATUS
approved