A379632 Irregular triangle read by rows in which row n lists the smallest parts of the partitions of n into consecutive parts (with the partitions ordered by increasing number of parts).

1, 2, 3, 1, 4, 5, 2, 6, 1, 7, 3, 8, 9, 4, 2, 10, 1, 11, 5, 12, 3, 13, 6, 14, 2, 15, 7, 4, 1, 16, 17, 8, 18, 5, 3, 19, 9, 20, 2, 21, 10, 6, 1, 22, 4, 23, 11, 24, 7, 25, 12, 3, 26, 5, 27, 13, 8, 2, 28, 1, 29, 14, 30, 9, 6, 4, 31, 15, 32, 33, 16, 10, 3, 34, 7, 35, 17, 5, 2, 36, 11, 1, 37, 18, 38, 8, 39, 19, 12, 4, 40, 6, 41, 20

Offset: 1

Author

Omar E. Pol, Dec 31 2024

Keywords

• nonn
• tabf

Comments

Row n gives the first A001227(n) terms of the n-th row of A379630.

Examples

			Triangle begins:
   1;
   2;
   3,  1;
   4;
   5,  2;
   6,  1;
   7,  3;
   8;
   9,  4,  2;
  10,  1;
  11,  5;
  12,  3;
  13,  6;
  14,  2;
  15,  7,  4,  1;
  16;
  17,  8;
  18,  5,  3;
  19,  9;
  20,  2;
  21, 10,  6,  1;
  22,  4;
  23, 11;
  24,  7;
  25, 12,  3;
  26,  5;
  27, 13,  8,  2;
  28,  1;
  ...
Illustration of initial terms:
                                                         _
                                                       _|1|
                                                     _|2 _|
                                                   _|3  |1|
                                                 _|4   _| |
                                               _|5    |2 _|
                                             _|6     _| |1|
                                           _|7      |3  | |
                                         _|8       _|  _| |
                                       _|9        |4  |2 _|
                                     _|10        _|   | |1|
                                   _|11         |5   _| | |
                                 _|12          _|   |3  | |
                               _|13           |6    |  _| |
                             _|14            _|    _| |2 _|
                           _|15             |7    |4  | |1|
                         _|16              _|     |   | | |
                       _|17               |8     _|  _| | |
                     _|18                _|     |5  |3  | |
                   _|19                 |9      |   |  _| |
                 _|20                  _|      _|   | |2 _|
               _|21                   |10     |6   _| | |1|
             _|22                    _|       |   |4  | | |
           _|23                     |11      _|   |   | | |
         _|24                      _|       |7    |  _| | |
       _|25                       |12       |    _| |3  | |
     _|26                        _|        _|   |5  |  _| |
   _|27                         |13       |8    |   | |2 _|
  |28                           |         |     |   | | |1|
  ...
The diagram is also the left part of the diagram of A379630.
The geometrical structure is the same as the diagram of A237591.
		

Crossrefs

Positive terms of A211343.

Absolute values of A341971.

Column 1 gives A000027.

Right border gives A118235.

Row lengths give A001227.

Row sums give A286014.

Subsequence of A286001 and of A299765 and of A379630.

For the largest parts see A379633.

Cf. A196020, A235791, A236104, A237048, A237591, A237593, A245092, A262626, A379631, A379634.