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A196931
Triangle read by rows in which row n lists in nondecreasing order the smallest part of every partition of n.
9
0, 1, 1, 2, 1, 1, 3, 1, 1, 1, 2, 4, 1, 1, 1, 1, 1, 2, 5, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,4
COMMENTS
If n >= 1, row n lists the smallest parts of every partition of n in the order produced by the shell model of partitions of A135010, hence row n lists the parts of the last section of the set of partitions of n, except the emergent parts (See A182699).
Row n has length A000041(n). Row sums give A046746. Right border of triangle gives A001477. Row n starts with A000041(n-1) ones, n >= 1.
EXAMPLE
Written as a triangle:
0,
1,
1,2,
1,1,3,
1,1,1,2,4,
1,1,1,1,1,2,5,
1,1,1,1,1,1,1,2,2,3,6
1,1,1,1,1,1,1,1,1,1,1,2,2,3,7,
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,4,8,
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Oct 21 2011
STATUS
approved