A211980 Triangle read by rows: T(n,k) = total number of regions in the last n-k+1 shells of n.

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

Author

Omar E. Pol, Apr 27 2012

Keywords

• nonn
• tabl

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.

Examples

			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;
		

Links

• Omar E. Pol, Illustration of the seven regions of 5

Crossrefs

Mirror of triangle A211990. Column 1 is A000041, n >= 1. Right border is A187219.

Cf. A135010, A138121, A182703, A186114, A206437, A212000, A212001.

Formula

T(n,1) = A000041(n).

T(n,k) = A000041(n) - A000041(k-1), 1

T(n,k) = Sum_{j=k..n} A187219(j).

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.