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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
OFFSET
1,2
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)
Sequence in context: A241773 A348388 A205790 * A235791 A035426 A065516
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Dec 19 2016
STATUS
approved