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A210972
Sum of all region numbers of all parts of all partitions of n.
3
1, 5, 14, 43, 98, 255, 532, 1201, 2413, 4968, 9427, 18475
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.
EXAMPLE
For n = 5 we have:
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. Two arrangements
k of the partitions of 5
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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]
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. Two arrangements
. of the region numbers Sum of
k of the partitions of 5 zone k
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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
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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
Partial sums of A210969. Row sums of triangle A210971.
Sequence in context: A034549 A232492 A180774 * A197607 A296829 A102434
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Jun 30 2012
STATUS
approved