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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.

%I A279820 #22 Apr 18 2017 16:32:33
%S A279820 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,
%T A279820 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,
%U A279820 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
%N 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.
%e A279820 Triangle begins:
%e A279820 1;
%e A279820 2;
%e A279820 3, 1;
%e A279820 4, 1;
%e A279820 5, 2;
%e A279820 5, 1, 2;
%e A279820 6, 1, 3;
%e A279820 7, 1, 3:
%e A279820 7, 2, 4;
%e A279820 8, 2, 1, 3;
%e A279820 9, 2, 1, 4;
%e A279820 ...
%e A279820 Illustration of initial terms:
%e A279820 Row                                           _
%e A279820 1                                           _|1|
%e A279820 2                                         _|2  |_
%e A279820 3                                       _|3    |1|
%e A279820 4                                     _|4      |1|_
%e A279820 5                                   _|5       _|  2|
%e A279820 6                                 _|5        |1|  2|_
%e A279820 7                               _|6          |1|    3|
%e A279820 8                             _|7           _|1|    3|_
%e A279820 9                           _|7            |2  |_     4|
%e A279820 10                        _|8              |2  |1|    3|_
%e A279820 11                      _|9               _|2  |1|      4|
%e A279820 12                    _|9                |3    |1|      4|_
%e A279820 13                  _|10                 |3    |1|_       5|
%e A279820 14                _|11                  _|3   _|  2|      4|_
%e A279820 15              _|11                   |3    |1|  2|        5|
%e A279820 16            _|12                     |3    |1|  2|        5|_
%e A279820 17          _|13                      _|3    |1|  2|_         6|
%e A279820 18        _|13                       |4      |1|    3|        5|_
%e A279820 19      _|14                         |4     _|1|    3|          6|
%e A279820 20    _|15                          _|3    |2  |_   3|          6|_
%e A279820 21   |15                           |4      |2  |1|  2|            7|
%e A279820 ...
%e A279820 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].
%e A279820 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.
%Y A279820 Row sums give A001651.
%Y A279820 Row n has length A003056(n) hence column k starts in row A000217(k)
%Y A279820 Cf. A001227, A196020, A235791, A236104, A237048, A237591, A237593, A245092, A259176, A261699, A262626.
%K A279820 nonn,tabf
%O A279820 1,2
%A A279820 _Omar E. Pol_, Dec 19 2016