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A182377
Total sum of positive ranks of all regions in the last shell of n.
2
0, 0, 0, 1, 2, 5, 8, 14, 21, 32, 45, 67, 91
OFFSET
1,5
COMMENTS
The rank of a region of n is the largest part minus the number of parts. For the definition of "region of n" see A206437. For the definition of "last shell of n" see A135010.
a(n) is also the sum of positive integers in row n of triangle A194447. First differs from A000094 at a(12).
EXAMPLE
For n = 7 the last shell of 7 contains four regions: [3],[5,2],[4],[7,3,2,2,1,1,1,1,1,1,1,1,1,1,1] so we have:
----------------------------------------------------------
. Largest Number
Region part of parts Rank
----------------------------------------------------------
. 1 3 1 2
. 2 5 2 3
. 3 4 1 3
. 4 7 15 -8
.
The sum of positive ranks is a(7) = 2 + 3 + 3 = 8.
KEYWORD
nonn,more
AUTHOR
Omar E. Pol, Apr 29 2012
STATUS
approved