cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A379633 Irregular triangle read by rows in which row n lists the largest parts of the partitions of n into consecutive parts (with the partitions ordered by increasing number of parts).

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%I A379633 #23 Jan 07 2025 10:13:40
%S A379633 1,2,3,2,4,5,3,6,3,7,4,8,9,5,4,10,4,11,6,12,5,13,7,14,5,15,8,6,5,16,
%T A379633 17,9,18,7,6,19,10,20,6,21,11,8,6,22,7,23,12,24,9,25,13,7,26,8,27,14,
%U A379633 10,7,28,7,29,15,30,11,9,8,31,16,32,33,17,12,8,34,10,35,18,9,8,36,13,8,37,19,38,11,39,20,14,9,40,10,41,21
%N A379633 Irregular triangle read by rows in which row n lists the largest parts of the partitions of n into consecutive parts (with the partitions ordered by increasing number of parts).
%C A379633 Row n gives the first A001227(n) terms of the n-th row of A379631.
%C A379633 Conjecture: the right border gives A212652.
%e A379633 Triangle begins:
%e A379633    1;
%e A379633    2;
%e A379633    3,  2;
%e A379633    4;
%e A379633    5,  3;
%e A379633    6,  3;
%e A379633    7,  4;
%e A379633    8;
%e A379633    9,  5,  4;
%e A379633   10,  4;
%e A379633   11,  6;
%e A379633   12,  5;
%e A379633   13,  7;
%e A379633   14,  5;
%e A379633   15,  8,  6,  5;
%e A379633   16;
%e A379633   17,  9;
%e A379633   18,  7,  6;
%e A379633   19, 10;
%e A379633   20,  6;
%e A379633   21, 11,  8,  6;
%e A379633   22,  7;
%e A379633   23, 12;
%e A379633   24,  9;
%e A379633   25, 13,  7;
%e A379633   26,  8;
%e A379633   27, 14, 10,  7;
%e A379633   28,  7;
%e A379633   ...
%e A379633 Illustration of initial terms:
%e A379633                                                          _
%e A379633                                                        _|1|
%e A379633                                                      _|2 _|
%e A379633                                                    _|3  |2|
%e A379633                                                  _|4   _| |
%e A379633                                                _|5    |3 _|
%e A379633                                              _|6     _| |3|
%e A379633                                            _|7      |4  | |
%e A379633                                          _|8       _|  _| |
%e A379633                                        _|9        |5  |4 _|
%e A379633                                      _|10        _|   | |4|
%e A379633                                    _|11         |6   _| | |
%e A379633                                  _|12          _|   |5  | |
%e A379633                                _|13           |7    |  _| |
%e A379633                              _|14            _|    _| |5 _|
%e A379633                            _|15             |8    |6  | |5|
%e A379633                          _|16              _|     |   | | |
%e A379633                        _|17               |9     _|  _| | |
%e A379633                      _|18                _|     |7  |6  | |
%e A379633                    _|19                 |10     |   |  _| |
%e A379633                  _|20                  _|      _|   | |6 _|
%e A379633                _|21                   |11     |8   _| | |6|
%e A379633              _|22                    _|       |   |7  | | |
%e A379633            _|23                     |12      _|   |   | | |
%e A379633          _|24                      _|       |9    |  _| | |
%e A379633        _|25                       |13       |    _| |7  | |
%e A379633      _|26                        _|        _|   |8  |  _| |
%e A379633    _|27                         |14       |10   |   | |7 _|
%e A379633   |28                           |         |     |   | | |7|
%e A379633   ...
%e A379633 The diagram is also the left part of the diagram of A379631.
%e A379633 The geometrical structure is the same as the diagram of A237591.
%Y A379633 Positive terms of A286013.
%Y A379633 Column 1 gives A000027.
%Y A379633 Row lengths give A001227.
%Y A379633 Row sums give A286015.
%Y A379633 Subsequence of A286000 and of A299765 and of A379631.
%Y A379633 For the smallest parts see A379632.
%Y A379633 Cf. A196020, A212652, A235791, A236104, A237048, A237591, A237593, A245092, A262626, A379630, A379634.
%K A379633 nonn,tabf
%O A379633 1,2
%A A379633 _Omar E. Pol_, Dec 31 2024