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, 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

Offset: 1

Author

Omar E. Pol, Dec 19 2016

Keywords

• nonn
• tabf

Examples

			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.