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

1,2

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: A241773 A348388 A205790 * A235791 A035426 A065516

Adjacent sequences: A279817 A279818 A279819 * A279821 A279822 A279823

Keyword

nonn,tabf

Author

Omar E. Pol, Dec 19 2016

Status

approved