cp's OEIS Frontend

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).

%I A379632 #28 Jan 07 2025 10:12:31
%S A379632 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,
%T A379632 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,
%U A379632 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
%N 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).
%C A379632 Row n gives the first A001227(n) terms of the n-th row of A379630.
%e A379632 Triangle begins:
%e A379632    1;
%e A379632    2;
%e A379632    3,  1;
%e A379632    4;
%e A379632    5,  2;
%e A379632    6,  1;
%e A379632    7,  3;
%e A379632    8;
%e A379632    9,  4,  2;
%e A379632   10,  1;
%e A379632   11,  5;
%e A379632   12,  3;
%e A379632   13,  6;
%e A379632   14,  2;
%e A379632   15,  7,  4,  1;
%e A379632   16;
%e A379632   17,  8;
%e A379632   18,  5,  3;
%e A379632   19,  9;
%e A379632   20,  2;
%e A379632   21, 10,  6,  1;
%e A379632   22,  4;
%e A379632   23, 11;
%e A379632   24,  7;
%e A379632   25, 12,  3;
%e A379632   26,  5;
%e A379632   27, 13,  8,  2;
%e A379632   28,  1;
%e A379632   ...
%e A379632 Illustration of initial terms:
%e A379632                                                          _
%e A379632                                                        _|1|
%e A379632                                                      _|2 _|
%e A379632                                                    _|3  |1|
%e A379632                                                  _|4   _| |
%e A379632                                                _|5    |2 _|
%e A379632                                              _|6     _| |1|
%e A379632                                            _|7      |3  | |
%e A379632                                          _|8       _|  _| |
%e A379632                                        _|9        |4  |2 _|
%e A379632                                      _|10        _|   | |1|
%e A379632                                    _|11         |5   _| | |
%e A379632                                  _|12          _|   |3  | |
%e A379632                                _|13           |6    |  _| |
%e A379632                              _|14            _|    _| |2 _|
%e A379632                            _|15             |7    |4  | |1|
%e A379632                          _|16              _|     |   | | |
%e A379632                        _|17               |8     _|  _| | |
%e A379632                      _|18                _|     |5  |3  | |
%e A379632                    _|19                 |9      |   |  _| |
%e A379632                  _|20                  _|      _|   | |2 _|
%e A379632                _|21                   |10     |6   _| | |1|
%e A379632              _|22                    _|       |   |4  | | |
%e A379632            _|23                     |11      _|   |   | | |
%e A379632          _|24                      _|       |7    |  _| | |
%e A379632        _|25                       |12       |    _| |3  | |
%e A379632      _|26                        _|        _|   |5  |  _| |
%e A379632    _|27                         |13       |8    |   | |2 _|
%e A379632   |28                           |         |     |   | | |1|
%e A379632   ...
%e A379632 The diagram is also the left part of the diagram of A379630.
%e A379632 The geometrical structure is the same as the diagram of A237591.
%Y A379632 Positive terms of A211343.
%Y A379632 Absolute values of A341971.
%Y A379632 Column 1 gives A000027.
%Y A379632 Right border gives A118235.
%Y A379632 Row lengths give A001227.
%Y A379632 Row sums give A286014.
%Y A379632 Subsequence of A286001 and of A299765 and of A379630.
%Y A379632 For the largest parts see A379633.
%Y A379632 Cf. A196020, A235791, A236104, A237048, A237591, A237593, A245092, A262626, A379631, A379634.
%K A379632 nonn,tabf
%O A379632 1,2
%A A379632 _Omar E. Pol_, Dec 31 2024