A194853 Pair(i,j): a folded version of the shell model of partitions (see comments for precise definition).

0, 1, 0, 2, -2, 1, 0, 2, 0, 4, -1, 2, -4, 1, 0, 2, -2, 2, 0, 3, 0, 6

Offset: 1

Author

Omar E. Pol, Feb 12 2012

Keywords

• sign
• more

Comments

In the shell model of partitions (Cf. A135010, A138121) the n-th largest part has length = A141285(n). After the folding of the partitions the pair(i,j) shows the horizontal location of the n-th largest part at the level n of the structure (see example).

Examples

			-------------------------------------------
                  Pair      The structure
n   A141285(n)   (i, j)    looks like this
-------------------------------------------
1       1         0, 1,           *
2       2         0, 2,           **
3       3        -2, 1,         ***
4       2         0, 2,           **
5       4         0, 4,           ****
6       3        -1, 2,          ***
7       5        -4, 1        *****
8       2         0, 2            **
9       4        -2, 2          ****
10      3         0, 3            ***
11      6         0, 6            ******
		

Links

• Omar E. Pol, Illustration of the shell model of partitions before of the folding of all partitions (for integers = 1..12)

Crossrefs

Cf. A135010, A138121, A141285.

Formula

A141285(n) = abs(i(n)) + j(n).