OFFSET
1,2
COMMENTS
Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.
LINKS
EXAMPLE
For n = 5 we have:
---------------------------------------------------
. Two arrangements
k of the partitions of 5
---------------------------------------------------
7 [5] [5]
6 [3+2] [3+2]
5 [4+1] [4 +1]
4 [2+1+1] [2+2 +1]
3 [3+1+1] [3 +1 +1]
2 [2+1+1+1] [2+1 +1 +1]
1 [1+1+1+1+1] [1+1+1 +1 +1]
---------------------------------------------------
. Two arrangements
. of the region numbers Sum of
k of the partitions of 5 zone k
---------------------------------------------------
7 [7] [7] 7
6 [6,7] [6,7] 13
5 [5,7] [5, 7] 12
4 [4,5,7] [4,5, 7] 16
3 [3,5,7] [3, 5, 7] 15
2 [2,3,5,7] [2,3, 5, 7] 17
1 [1,2,3,5,7] [1,2,3, 5, 7] 18
---------------------------------------------------
The total sum is a(5) = 1+2^2+3^2+4+5^2+6+7^2 = 1+4+9+4+25+6+49 = 18+17+15+16+12+13+7 = 98.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Jun 30 2012
STATUS
approved