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A275601
Triangle read by rows which is constructed with the diagram of the isosceles triangle of A279693 and filling the empty cells with zeros.
4
1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
COMMENTS
For the construction of this triangle we start with the diagram of A237048. Then with the diagram of the isosceles triangle of A279693 as shown below:
Row _ _
1 _|1|1|_
2 _|1 _|_ 1|_
3 _|1 |1|1| 1|_
4 _|1 _|0|0|_ 1|_
5 _|1 |1 _|_ 1| 1|_
6 _|1 _|0|1|1|0|_ 1|_
7 _|1 |1 |0|0| 1| 1|_
8 _|1 _|0 _|0|0|_ 0|_ 1|_
9 _|1 |1 |1 _|_ 1| 1| 1|_
10 _|1 _|0 |0|1|1|0| 0|_ 1|_
11 _|1 |1 _|0|0|0|0|_ 1| 1|_
12 _|1 _|0 |1 |0|0| 1| 0|_ 1|_
13 _|1 |1 |0 _|0|0|_ 0| 1| 1|_
14 _|1 _|0 _|0|1 _|_ 1|0|_ 0|_ 1|_
15 _|1 |1 |1 |0|1|1|0| 1| 1| 1|_
16 |1 |0 |0 |0|0|0|0| 0| 0| 1|
...
And then filling with zeros the empty cells of the structure, as shown below:
Illustration of initial terms as an isosceles triangle:
Row _ _
1 _|1 1|_
2 _|1 0 0 1|_
3 _|1 0 1 1 0 1|_
4 _|1 0 0 0 0 0 0 1|_
5 _|1 0 0 1 0 0 1 0 0 1|_
6 _|1 0 0 0 0 1 1 0 0 0 0 1|_
7 _|1 0 0 0 1 0 0 0 0 1 0 0 0 1|_
8 _|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|_
9 _|1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1|_
10 _|1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1|_
11 _|1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1|_
12 _|1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1|_
13 _|1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1|_
14 _|1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1|_
15 _|1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1|_
16 |1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|
...
Note that the mentioned triangles are related to isosceles triangle A237593 and to the front view of the pyramid described in A245092.
The position of the 1's in the n-th row of the diagram is related to the subparts of the symmetric representation of sigma(n). For more information see A279387, A281010 and A281011.
For a right triangle which is the left hand part of this triangle see A279733.
EXAMPLE
Triangle begins:
1, 1;
1, 0, 0, 1;
1, 0, 1, 1, 0, 1;
1, 0, 0, 0, 0, 0, 0, 1;
1, 0, 0, 1, 0, 0, 1, 0, 0, 1;
1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1;
1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
...
CROSSREFS
Absolute values of A281011.
Row n has length 2n.
Row sums give A054844.
One half of row sums gives A001227.
Sequence in context: A246142 A091219 A304109 * A281011 A016416 A014024
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 17 2016
STATUS
approved