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 (0<=k<=n) begins: 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 0, 4, 2, 2, 1, 1, 0, 0, 4, 4, 2, 2, 1, 1, 0, 0, 7, 4, 4, 2, 2, 1, 1, 0, 0, 8, 7, 4, 4, 2, 2, 1, 1, 0, 0,
For n=1 the unique partition of 2n that does not contains 1 as part is 2, so row 1 has an element = 2. For n=2 there are 2 partitions of 2n that do not contain 1 as part: 4 ............ or ....... 4 . . . 2 + 2 ........ or .......(2). 2 . These partitions contain (2), the row n-1 of triangle, so the parts of the largest subshell are 4, 2. For n=3 there are 4 partitions of 2n that do not contain 1 as part: 6 ............ or ....... 6 . . . . . 3 + 3 ........ or ....... 3 . . 3 . . 4 + 2 ........ or .......(4). . . 2 . 2 + 2 + 2 .... or .......(2).(2). 2 . These partitions contain (4) and (2),(2), the parts of rows < n of triangle, so the parts of the largest subshell are 6, 3, 3, 2, 2. And so on. Triangle begins: 2, 4, 2, 6, 3, 3, 2, 2, 8, 4, 4, 5, 3, 2, 2, 2, 2, 10, 5, 5, 6, 4, 7, 3, 4, 3, 3, 2, 2, 2, 2, 2, 2, 2,
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