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A210969
Sum of all region numbers of all parts of the last section of the set of partitions of n.
3
1, 4, 9, 29, 55, 157, 277, 669, 1212, 2555, 4459, 9048
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.
The last section of the set of partitions of n is also the n-th section of the set of partitions of any integer >= n. - Omar E. Pol, Apr 07 2014
EXAMPLE
For n = 6 the four regions of the last section of 6 are [2], [4, 2], [3], [6, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1] therefore the "region numbers" are [8], [9, 9], [10], [11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11]. The sum of all region numbers is a(6) = 8+2*9+10+11^2 = 8+18+10+121 = 157, see below:
--------------------------------------------
. Last section Sum of
. of the set of Region region
k partitions of 6 numbers numbers
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11 6 11 11
10 3+3 10,11 21
9 4 +2 9, 11 20
8 2+2 +2 8,9, 11 28
7 1 11 11
6 1 11 11
5 1 11 11
4 1 11 11
3 1 11 11
2 1 11 11
1 1 11 11
--------------------------------------------
Total sum of region numbers is a(6) = 157
CROSSREFS
Row sums of triangle A210966. Partial sums give A210972.
Sequence in context: A069563 A352878 A276984 * A059345 A127768 A231255
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Jul 01 2012
STATUS
approved