A182740 A shell model of partitions as a table of partitions.

1, 2, 1, 3, 0, 1, 2, 0, 1, 1, 4, 0, 0, 1, 1

Offset: 1

Author

Omar E. Pol, Nov 30 2010

Keywords

• nonn
• tabl
• more

Comments

This array read by antidiagonals is a table of partitions for all integers.

For another version but as a binary code see A182741.

For more information see A135010 and A138121 which are the main entries for this sequence.

Examples

			For the numbers 1..6 the shell model of partitions has 6 shells. The model as a table looks like this:
1 1 1 1 1 1
2 . 1 1 1 1
3 . . 1 1 1
2 . 2 . 1 1
4 . . . 1 1
3 . . 2 . 1
5 . . . . 1
2 . 2 . 2 .
4 . . . 2 .
3 . . 3 . .
6 . . . . .
Then replace the dots by zeros.
Remarks: one number by column, for example 23 is located only in a column, not in two columns.
The table looks like this:
1 1 1 1 1 1
2 0 1 1 1 1
3 0 0 1 1 1
2 0 2 0 1 1
4 0 0 0 1 1
3 0 0 2 0 1
5 0 0 0 0 1
2 0 2 0 2 0
4 0 0 0 2 0
3 0 0 3 0 0
6 0 0 0 0 0
Array begins:
1,1,1,1,1,1,
2,0,1,1,1,
3,0,0,1,
2,0,2,
4,0,
3,
		

Links

• Omar E. Pol, Illustration of the shell model of partitions for 1..6 (2D-3D view)
• Omar E. Pol, Illustration of the shell model of partitions for 1..10 (2D view)
• Omar E. Pol Illustration of the shell model of partitions for 1..9 (3D view)

Crossrefs

Cf. A135010, A138121, A182741, A182742, A182743.