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A207379
Triangle read by rows: T(n,k) = number of parts that are in the k-th column of the last section of the set of partitions of n.
5
1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 4, 4, 3, 2, 1, 1, 4, 4, 4, 3, 2, 1, 1, 7, 7, 6, 5, 3, 2, 1, 1, 8, 8, 8, 6, 5, 3, 2, 1, 1, 12, 12, 11, 10, 7, 5, 3, 2, 1, 1, 14, 14, 14, 12, 10, 7, 5, 3, 2, 1, 1, 21, 21, 20, 18, 14, 11, 7, 5, 3, 2, 1, 1
OFFSET
1,7
COMMENTS
Note that for n >= 2 the tail of the last section of n starts at the second column and the second column contains only one part of size 1, thus both the first and the second columns contain the same number of parts. For more information see A135010 and A182703.
EXAMPLE
Illustration of initial terms. First six rows of triangle as numbers of parts in the columns from the last sections of the first six natural numbers:
. 6
. 3 3
. 4 2
. 2 2 2
. 5 1
. 3 2 1
. 4 1 1
. 2 2 1 1
. 3 1 1 1
. 2 1 1 1 1
1 1 1 1 1 1
---------------------------------------------------
1, 1,1, 1,1,1, 2,2,1,1, 2,2,2,1,1, 4,4,3,2,1,1
...
Triangle begins:
1;
1, 1;
1, 1, 1;
2, 2, 1, 1;
2, 2, 2, 1, 1;
4, 4, 3, 2, 1, 1;
4, 4, 4, 3, 2, 1, 1;
7, 7, 6, 5, 3, 2, 1, 1;
8, 8, 8, 6, 5, 3, 2, 1, 1;
12, 12, 11, 10, 7, 5, 3, 2, 1, 1;
14, 14, 14, 12, 10, 7, 5, 3, 2, 1, 1;
21, 21, 20, 18, 14, 11, 7, 5, 3, 2, 1, 1;
CROSSREFS
Column 1 is A187219. Row sums give A138137. Reversed rows converge to A000041.
Sequence in context: A291191 A273866 A071202 * A220163 A102715 A254687
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Mar 10 2012
STATUS
approved