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A279820 Irregular triangle read by rows in which T(n,k) is the number of cells in the k-th horizontal bar of the n-th row of a diagram which is similar to the diagram of A237591, but here the even-indexed zig-zag paths are in the right hand part of the structure. 1
1, 2, 3, 1, 4, 1, 5, 2, 5, 1, 2, 6, 1, 3, 7, 1, 3, 7, 2, 4, 8, 2, 1, 3, 9, 2, 1, 4, 9, 3, 1, 4, 10, 3, 1, 5, 11, 3, 2, 4, 11, 3, 1, 2, 5, 12, 3, 1, 2, 5, 13, 3, 1, 2, 6, 13, 4, 1, 3, 5, 14, 4, 1, 3, 6, 15, 3, 2, 3, 6, 15, 4, 2, 1, 2, 7, 16, 4, 2, 1, 3, 6, 17, 4, 2, 1, 3, 7, 17, 5, 2, 1, 3, 7, 18, 4, 3, 1, 3, 8, 19, 4, 3, 1, 4, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..106.

EXAMPLE

Triangle begins:

1;

2;

3, 1;

4, 1;

5, 2;

5, 1, 2;

6, 1, 3;

7, 1, 3:

7, 2, 4;

8, 2, 1, 3;

9, 2, 1, 4;

...

Illustration of initial terms:

Row                                           _

1                                           _|1|

2                                         _|2  |_

3                                       _|3    |1|

4                                     _|4      |1|_

5                                   _|5       _|  2|

6                                 _|5        |1|  2|_

7                               _|6          |1|    3|

8                             _|7           _|1|    3|_

9                           _|7            |2  |_     4|

10                        _|8              |2  |1|    3|_

11                      _|9               _|2  |1|      4|

12                    _|9                |3    |1|      4|_

13                  _|10                 |3    |1|_       5|

14                _|11                  _|3   _|  2|      4|_

15              _|11                   |3    |1|  2|        5|

16            _|12                     |3    |1|  2|        5|_

17          _|13                      _|3    |1|  2|_         6|

18        _|13                       |4      |1|    3|        5|_

19      _|14                         |4     _|1|    3|          6|

20    _|15                          _|3    |2  |_   3|          6|_

21   |15                           |4      |2  |1|  2|            7|

...

For n = 6 the 6th row of the diagram has three horizontal bars (or parts) that contain 5, 1 and 2 cells respectively, so the 6th row of the triangle is [5, 1, 2].

Note that the number of horizontal line segments in the n-th row of the structure equals A001227(n), the number of odd divisors of n.

CROSSREFS

Row sums give A001651.

Row n has length A003056(n) hence column k starts in row A000217(k)

Cf. A001227, A196020, A235791, A236104, A237048, A237591, A237593, A245092, A259176, A261699, A262626.

Sequence in context: A218534 A241773 A205790 * A235791 A035426 A065516

Adjacent sequences:  A279817 A279818 A279819 * A279821 A279822 A279823

KEYWORD

nonn,tabf

AUTHOR

Omar E. Pol, Dec 19 2016

STATUS

approved

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Last modified October 22 07:48 EDT 2019. Contains 328315 sequences. (Running on oeis4.)