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, 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
Examples
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;