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A211980
Triangle read by rows: T(n,k) = total number of regions in the last n-k+1 shells of n.
2
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
OFFSET
1,2
COMMENTS
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.
FORMULA
T(n,1) = A000041(n).
T(n,k) = A000041(n) - A000041(k-1), 1<k<=n.
T(n,k) = Sum_{j=k..n} A187219(j).
EXAMPLE
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;
CROSSREFS
Mirror of triangle A211990. Column 1 is A000041, n >= 1. Right border is A187219.
Sequence in context: A308509 A280514 A246105 * A171730 A131243 A038497
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Apr 27 2012
STATUS
approved