A182748
Triangle T(n,k) read by rows in which row n lists the first n terms of A002865, except the first term, in reverse order together with 0.
Original entry on oeis.org
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, 12, 8, 7, 4, 4, 2, 2, 1, 1, 0, 0
Offset: 0
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,
A182813
Triangle read by rows in which row n lists the parts of the largest subshell of all partitions of 2n+1 that do not contain 1 as a part.
Original entry on oeis.org
3, 5, 2, 7, 4, 3, 2, 2, 9, 5, 4, 6, 3, 3, 3, 3, 2, 2, 2, 2, 11, 6, 5, 7, 4, 8, 3, 4, 4, 3, 5, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 13, 7, 6, 8, 5, 9, 4, 5, 4, 4, 10, 3, 5, 5, 3, 6, 4, 3, 7, 3, 3, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 1
For n=1 the unique partition of 2n+1=3 that does not contains 1 as part is 3, so row 1 has an element = 3.
For n=2 there are 2 partitions of 2n+1=5 that do not contain 1 as part:
5 ............ or ....... 5 . . . .
3 + 2 ........ or .......(3). . 2 .
These partitions contain (3), the row n-1 of triangle, so
the parts of the largest subshell are 5, 2.
For n=3 there are 4 partitions of 2n+1=7 that do not contain 1 as part:
7 ............ or ....... 7 . . . . . .
4 + 3 ........ or ....... 4 . . . 3 . .
5 + 2 ........ or .......(5). . . . 2 .
3 + 2 + 2 .... or .......(3). .(2). 2 .
These partitions contain (5) and (3),(2), the parts of the rows < n of triangle, so the parts of the largest subshell are 7, 4, 3, 2, 2.
And so on.
Triangle begins:
3,
5,2,
7,4,3,2,2,
9,5,4,6,3,3,3,3,2,2,2,2,
11,6,5,7,4,8,3,4,4,3,5,3,3,2,2,2,2,2,2,2,2,
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