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A211980
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Triangle read by rows: T(n,k) = total number of regions in the last n-k+1 shells of n.
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2
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1, 2, 1, 3, 2, 1, 5, 4, 3, 2, 7, 6, 5, 4, 2, 11, 10, 9, 8, 6, 4, 15, 14, 13, 12, 10, 8, 4, 22, 21, 20, 19, 17, 15, 11, 7, 30, 29, 28, 27, 25, 23, 19, 15, 8, 42, 41, 40, 39, 37, 35, 31, 27, 20, 12, 56, 55, 54, 53, 51, 49, 45, 41, 34, 26, 14, 77, 76, 75
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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The set of partitions of n contains n shells and A000041(n) regions. For the definition of "last section of n" see A135010. For the definition of "region of n" see A206437.
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LINKS
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FORMULA
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EXAMPLE
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Triangle begins:
1;
2, 1;
3, 2, 1;
5, 4, 3, 2;
7, 6, 5, 4, 2;
11, 10, 9, 8, 6, 4;
15, 14, 13, 12, 10, 8, 4;
22, 21, 20, 19, 17, 15, 11, 7;
30, 29, 28, 27, 25, 23, 19, 15, 8;
42, 41, 40, 39, 37, 35, 31, 27, 20, 12;
56, 55, 54, 53, 51, 49, 45, 41, 34, 26, 14;
77, 76, 75, 74, 72, 70, 66, 62, 55, 47, 35, 21;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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