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A285574 Irregular triangle read by rows which arises from a diagram which is similar to the diagram of A261699, but here the even-indexed zig-zag lines are located on the right-hand side of the vertical axis of the diagram. 1
1, 1, 1, 3, 1, 0, 1, 5, 1, 3, 0, 1, 0, 7, 1, 0, 0, 1, 3, 9, 1, 0, 5, 0, 1, 0, 0, 11, 1, 3, 0, 0, 1, 0, 0, 13, 1, 0, 7, 0, 1, 3, 5, 0, 15, 1, 0, 0, 0, 0, 1, 0, 0, 0, 17, 1, 3, 0, 9, 0, 1, 0, 0, 0, 19, 1, 0, 5, 0, 0, 1, 3, 0, 7, 0, 21, 1, 0, 0, 0, 11, 0, 1, 0, 0, 0, 0, 23, 1, 3, 0, 0, 0, 0, 1, 0, 5, 0, 0, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

In the diagram we have that:

The number of horizontal line segments in the n-th row of the structure equals A001227(n), the number of partitions of n into consecutive parts.

The number of horizontal line segments in the left-hand part of the n-th row equals A082647, the number of partitions of n into an odd number of consecutive parts.

The number of horizontal line segments in the right-hand part of the n-th row equals A131576, the number of partitions of n into an even number of consecutive parts.

The diagram explains the unusual ordering of the terms in the triangle A261699, in which the even-indexed zig-zag lines are located on the left-hand side of the vertical axis of the diagram.

LINKS

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

EXAMPLE

Triangle begins:

1;

1;

1, 3;

1, 0,

1, 5;

1, 3, 0;

1, 0, 7;

1, 0, 0;

1, 3, 9;

1, 0, 5,  0;

1, 0, 0, 11;

1, 3, 0,  0;

1, 0, 0, 13;

1, 0, 7,  0;

1, 3, 5,  0, 15;

1, 0, 0,  0,  0;

1, 0, 0,  0, 17;

1, 3, 0,  9,  0;

1, 0, 0,  0, 19;

1, 0, 5,  0,  0;

1, 3, 0,  7,  0, 21;

...

Illustration of initial terms of the diagram:

Row                                           _

1                                           _|1|

2                                         _|1  |_

3                                       _|1    |3|

4                                     _|1      |0|_

5                                   _|1       _|  5|

6                                 _|1        |3|  0|_

7                               _|1          |0|    7|

8                             _|1           _|0|    0|_

9                           _|1            |3  |_     9|

10                        _|1              |0  |5|    0|_

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

12                    _|1                |3    |0|      0|_

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

14                _|1                   _|0   _|  7|      0|_

15              _|1                    |3    |5|  0|       15|

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

17          _|1                       _|0    |0|  0|_        17|

18        _|1                        |3      |0|    9|        0|_

19      _|1                          |0     _|0|    0|         19|

20    _|1                           _|0    |5  |_   0|          0|_

21   |1                            |3      |0  |7|  0|           21|

...

(Compare with the diagram of A261699.)

CROSSREFS

Positive terms give A182469.

Row n has length A003056(n).

The sum of row n is A000593(n).

Column k starts in row A000217(k).

The number of positive terms in row n is A001227(n).

Cf. A082647, A131576, A196020, A235791, A236104, A237048, A237591, A237593, A245092, A259176, A259177, A261699, A279820.

Sequence in context: A050143 A103495 A261699 * A081719 A327618 A121314

Adjacent sequences:  A285571 A285572 A285573 * A285575 A285576 A285577

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Apr 21 2017

STATUS

approved

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Last modified August 6 12:33 EDT 2020. Contains 336246 sequences. (Running on oeis4.)