A275601 Triangle read by rows which is constructed with the diagram of the isosceles triangle of A279693 and filling the empty cells with zeros.

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.

Links

Table of n, a(n) for n=1..100.

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.

Cf. A196020, A235791, A236104, A237048, A237270, A237271, A237591, A237593, A239657, A245092, A249351, A261699, A262611, A262626, A279387, A279693, A279733, A281010.

Sequence in context: A246142 A091219 A304109 * A281011 A016416 A014024

Adjacent sequences: A275598 A275599 A275600 * A275602 A275603 A275604

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 17 2016

Status

approved