A275601 - OEIS

A275601

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

%I #115 Apr 18 2017 16:32:15

%S 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,

%T 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,

%U 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

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

%C 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:

%C Row _ _

%C 1 _|1|1|_

%C 2 _|1 _|_ 1|_

%C 3 _|1 |1|1| 1|_

%C 4 _|1 _|0|0|_ 1|_

%C 5 _|1 |1 _|_ 1| 1|_

%C 6 _|1 _|0|1|1|0|_ 1|_

%C 7 _|1 |1 |0|0| 1| 1|_

%C 8 _|1 _|0 _|0|0|_ 0|_ 1|_

%C 9 _|1 |1 |1 _|_ 1| 1| 1|_

%C 10 _|1 _|0 |0|1|1|0| 0|_ 1|_

%C 11 _|1 |1 _|0|0|0|0|_ 1| 1|_

%C 12 _|1 _|0 |1 |0|0| 1| 0|_ 1|_

%C 13 _|1 |1 |0 _|0|0|_ 0| 1| 1|_

%C 14 _|1 _|0 _|0|1 _|_ 1|0|_ 0|_ 1|_

%C 15 _|1 |1 |1 |0|1|1|0| 1| 1| 1|_

%C 16 |1 |0 |0 |0|0|0|0| 0| 0| 1|

%C ...

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

%C Illustration of initial terms as an isosceles triangle:

%C Row _ _

%C 1 _|1 1|_

%C 2 _|1 0 0 1|_

%C 3 _|1 0 1 1 0 1|_

%C 4 _|1 0 0 0 0 0 0 1|_

%C 5 _|1 0 0 1 0 0 1 0 0 1|_

%C 6 _|1 0 0 0 0 1 1 0 0 0 0 1|_

%C 7 _|1 0 0 0 1 0 0 0 0 1 0 0 0 1|_

%C 8 _|1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1|_

%C 9 _|1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 1|_

%C 10 _|1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1|_

%C 11 _|1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1|_

%C 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|_

%C 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|_

%C 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|_

%C 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|_

%C 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|

%C ...

%C Note that the mentioned triangles are related to isosceles triangle A237593 and to the front view of the pyramid described in A245092.

%C 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.

%C For a right triangle which is the left hand part of this triangle see A279733.

%e Triangle begins:

%e 1, 1;

%e 1, 0, 0, 1;

%e 1, 0, 1, 1, 0, 1;

%e 1, 0, 0, 0, 0, 0, 0, 1;

%e 1, 0, 0, 1, 0, 0, 1, 0, 0, 1;

%e 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1;

%e 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1;

%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%e ...

%Y Absolute values of A281011.

%Y Row n has length 2n.

%Y Row sums give A054844.

%Y One half of row sums gives A001227.

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

%K nonn,tabf

%O 1

%A _Omar E. Pol_, Dec 17 2016