A330242 Sum of largest emergent parts of the partitions of n.
0, 0, 0, 2, 3, 9, 12, 24, 33, 54, 72, 112, 144, 210, 273, 379, 485, 661, 835, 1112, 1401, 1825, 2284, 2944, 3652, 4645, 5745, 7223, 8879, 11080, 13541, 16760, 20406, 25062, 30379, 37102, 44761, 54351, 65347, 78919, 94517, 113645, 135603, 162331, 193088, 230182, 272916, 324195, 383169, 453571
Offset: 1
Keywords
Examples
For n = 9 the diagram of
the partitions of 9 that
do not contain 1 as a part
is as shown below: Partitions
.
|_ _ _| | | | [3, 2, 2, 2]
|_ _ _ _ _| | | [5, 2, 2]
|_ _ _ _| | | [4, 3, 2]
|_ _ _ _ _ _ _| | [7, 2]
|_ _ _| | | [3, 3, 3]
|_ _ _ _ _ _| | [6, 3]
|_ _ _ _ _| | [5, 4]
|_ _ _ _ _ _ _ _ _| [9]
.
Note that the above diagram is also the "head" of the last section of the set of partitions of 9, where the "tail" is formed by A000041(9-1)= 22 1's.
The diagram of the
emergent parts is as
shown below: Emergent parts
.
|_ _ _| | | [3, 2, 2]
|_ _ _ _ _| | [5, 2]
|_ _ _ _| | [4, 3]
|_ _ _ _ _ _ _| [7]
|_ _ _| | [3, 3]
|_ _ _ _ _ _| [6]
|_ _ _ _ _| [5]
.
The sum of the largest emergent parts is 3 + 5 + 4 + 7 + 3 + 6 + 5 = 33, so a(9) = 33.
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