A244580 Square array read by antidiagonals related to the symmetric representation of sigma.

1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 5, 4, 4, 4, 5, 6, 5, 4, 4, 5, 6, 7, 6, 5, 6, 5, 6, 7, 8, 7, 6, 6, 6, 6, 7, 8, 9, 8, 7, 6, 6, 6, 7, 8, 9, 10, 9, 8, 7, 8, 8, 7, 8, 9, 10, 11, 10, 9, 8, 8, 8, 8, 8, 9, 10, 11, 12, 11, 10, 9, 8, 9, 9, 8, 9, 10, 11, 12

Offset: 1

Author

Omar E. Pol, Jul 04 2014

Keywords

• nonn
• tabl

Comments

The number of parts k in the square array is equal to A000203(k) hence the sum of parts k is equal to A064987(k).

The structure has a three-dimensional representation using polycubes. T(n,k) is the height of a column. The total area in the horizontal level z gives A000203(z).

The main diagonal gives A244367.

Examples

			.                         _ _ _ _ _ _ _ _ _
1,2,3,4,5,6,7,8,9...     |_| | | | | | | | |
2,2,3,4,5,6,7,8,9...     |_ _|_| | | | | | |
3,3,4,4,5,6,7,8,9...     |_ _|  _|_| | | | |
4,4,4,6,6,6,7,8,9...     |_ _ _|    _|_| | |
5,5,5,6,6,8,8,8,9...     |_ _ _|  _|  _ _|_|
6,6,6,6,8,8,9...         |_ _ _ _|  _| |
7,7,7,7,8,9,9...         |_ _ _ _| |_ _|
8,8,8,8,8...             |_ _ _ _ _|
9,9,9,9,9...             |_ _ _ _ _|
.
		

Crossrefs

Cf. A000203, A064987, A143128, A185283, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A071562, A244367.