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A211025
Triangle read by rows: T(n,k) = total sum of parts in the last section of the set of partitions of n after k-th stage.
2
1, 1, 3, 1, 2, 5, 1, 2, 3, 5, 7, 11, 1, 2, 3, 4, 5, 7, 10, 15, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 19, 22, 25, 31, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 18, 20, 25, 28, 32, 39, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 19, 21, 23, 25, 27
OFFSET
1,3
COMMENTS
Also triangle read by rows in which row n lists the partial sums of row n of triangle A135010.
This triangle shows the growth of the last sections of the partitions of n step by step. At stage k one part of size A135010(n,k) is added to the structure of the n-th shell.
EXAMPLE
For row n = 5 of triangle we have:
-------------------------------------
Column Zone The 5th Total sum
k shell of parts
-------------------------------------
8 <> 7 (5) 15
7 <> 6 (3... 10
6 = 6 ...2) 7
5 = 5 (1) 5
4 = 4 (1) 4
3 = 3 (1) 3
2 = 2 (1) 2
1 = 1 (1) 1
.
Triangle begins:
1;
1,3;
1,2,5;
1,2,3,5,7,11;
1,2,3,4,5,7,10,15;
1,2,3,4,5,6,7,9,11,13,15,19,22,25,31;
1,2,3,4,5,6,7,8,9,10,11,13,15,18,20,25,28,32,39;
CROSSREFS
Row n has length A138137(n). Right border gives A138879.
Sequence in context: A123375 A021036 A354348 * A125704 A357498 A131127
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Apr 25 2012
STATUS
approved