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A182285 Triangle read by rows: T(n,k) = sum of all parts in the k-th zone of the last section of the set of partitions of n. 1
1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 4, 1, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 1, 1, 1, 6, 6, 6, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 7, 7, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 8, 8, 8, 8, 8, 8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row n lists A000041(n-1) 1's together with A002865(n) n's.
LINKS
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 of 7 the parts are 3, 2, 2, therefore T(7,12) = 3+2+2 = 7.
Written as a triangle begins:
1;
1,2;
1,1,3;
1,1,1,4,4;
1,1,1,1,1,5,5;
1,1,1,1,1,1,1,6,6,6,6;
1,1,1,1,1,1,1,1,1,1,1,7,7,7,7;
1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,8,8,8,8,8,8,8;
CROSSREFS
Row n has length A000041(n). Row sums give A138879.
Sequence in context: A108888 A124021 A109626 * A160182 A195825 A098824
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 23 2012
STATUS
approved

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Last modified July 23 08:23 EDT 2024. Contains 374546 sequences. (Running on oeis4.)