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.
Triangle begins:
1;
2;
2, 3;
5;
6, 7;
6, 11;
14, 15;
22;
25, 29, 30;
25, 42;
55, 56;
...
For n = 9 the partitions of 9 into consecutive parts are [4, 3, 2], [5, 4] and [9]. Then we have that in the list of colexicographically ordered partitions of 9 these partitions are in the rows 25, 29 and 30 respectively as shown below, so the 9th row of the triangle is [25, 29, 30].
--------------------------------------------------------
p Diagram Partitions of 9
--------------------------------------------------------
1 2 3 4 5 6 7 8 9
_ _ _ _ _ _ _ _ _
1 |_| | | | | | | | | [1, 1, 1, 1, 1, 1, 1, 1, 1]
2 |_ _| | | | | | | | [2, 1, 1, 1, 1, 1, 1, 1]
3 |_ _ _| | | | | | | [3, 1, 1, 1, 1, 1, 1]
4 |_ _| | | | | | | [2, 2, 1, 1, 1, 1, 1]
5 |_ _ _ _| | | | | | [4, 1, 1, 1, 1, 1]
6 |_ _ _| | | | | | [3, 2, 1, 1, 1, 1]
7 |_ _ _ _ _| | | | | [5, 1, 1, 1, 1]
8 |_ _| | | | | | [2, 2, 2, 1, 1, 1]
9 |_ _ _ _| | | | | [4, 2, 1, 1, 1]
10 |_ _ _| | | | | [3, 3, 1, 1, 1]
11 |_ _ _ _ _ _| | | | [6, 1, 1, 1]
12 |_ _ _| | | | | [3, 2, 2, 1, 1]
13 |_ _ _ _ _| | | | [5, 2, 1, 1]
14 |_ _ _ _| | | | [4, 3, 1, 1]
15 |_ _ _ _ _ _ _| | | [7, 1, 1]
16 |_ _| | | | | [2, 2, 2, 2, 1]
17 |_ _ _ _| | | | [4, 2, 2, 1]
18 |_ _ _| | | | [3, 3, 2, 1]
19 |_ _ _ _ _ _| | | [6, 2, 1]
20 |_ _ _ _ _| | | [5, 3, 1]
21 |_ _ _ _| | | [4, 4, 1]
22 |_ _ _ _ _ _ _ _| | [8, 1]
23 |_ _ _| | | | [3, 2, 2, 2]
24 |_ _ _ _ _| | | [5, 2, 2]
25 |_ _ _ _| | | [4, 3, 2] <--- Consecutive parts
26 |_ _ _ _ _ _ _| | [7, 2]
27 |_ _ _| | | [3, 3, 3]
28 |_ _ _ _ _ _| | [6, 3]
29 |_ _ _ _ _| | [5, 4] <--- Consecutive parts
30 |_ _ _ _ _ _ _ _ _| [9] <--- Consecutive parts
.
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