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A182284
Triangle read by rows: T(n,k) = number of parts in the k-th zone of the last section of the set of partitions of n.
1
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 3, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
1,10
EXAMPLE
Illustration of three arrangements of the last section of the set of partitions of 7 and the zone numbers:
--------------------------------------------------------
Zone \ a) b) c)
--------------------------------------------------------
15 (7) (7) (. . . . . . 7)
14 (4+3) (4+3) (. . . 4 . . 3)
13 (5+2) (5+2) (. . . . 5 . 2)
12 (3+2+2) (3+2+2) (. . 3 . 2 . 2)
11 (1) (1) (1)
10 (1) (1) (1)
9 (1) (1) (1)
8 (1) (1) (1)
7 (1) (1) (1)
6 (1) (1) (1)
5 (1) (1) (1)
4 (1) (1) (1)
3 (1) (1) (1)
2 (1) (1) (1)
1 (1) (1) (1)
.
For n = 7 and k = 12 we can see that in the 12th zone of the last section there are three parts: 3, 2, 2, therefore T(7,12) = 3.
Written as a triangle begins:
1;
1,1;
1,1,1;
1,1,1,2,1;
1,1,1,1,1,2,1;
1,1,1,1,1,1,1,3,2,2,1;
1,1,1,1,1,1,1,1,1,1,1,3,2,2,1;
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4,3,3,2,2,2,1;
CROSSREFS
Row n has length A000041(n). Row sums give A138137.
Sequence in context: A119849 A246588 A026492 * A139551 A022931 A373217
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 23 2012
STATUS
approved