A358120 Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened.

1, 1, 1, 2, 1, 3, 2, 1, 4, 3, 5, 2, 1, 6, 5, 8, 3, 7, 2, 4, 1, 9, 7, 13, 5, 11, 8, 10, 3, 12, 2, 6, 4, 1, 14, 11, 20, 9, 18, 13, 21, 5, 16, 12, 15, 3, 19, 7, 17, 2, 8, 6, 10, 4, 1, 22, 17, 32, 13, 30, 21, 34, 9, 26, 19, 33, 15, 24, 18, 28, 5, 23, 20, 29, 3, 27, 11, 31, 7, 25, 2, 12, 10, 16, 6, 14, 4, 8

Offset: 1

Author

Rémy Sigrist, Oct 30 2022

Keywords

• nonn
• tabf

Comments

The n-th row contains A000045(n) terms, and is a permutation of 1..A000045(n).

Examples

			Table begins:
    1,
    1,
    1, 2,
    1, 3, 2,
    1, 4, 3, 5, 2,
    1, 6, 5, 8, 3, 7, 2, 4,
    1, 9, 7, 13, 5, 11, 8, 10, 3, 12, 2, 6, 4,
    ...
For n = 7:
- terms in rows 6 and 5 are: 1, 6, 5, 8, 3, 7, 2, 4, 1, 4, 3, 5, 2,
- positions of 1's are: 1, 9,
- positions of 2's are: 7, 13,
- positions of 3's are: 5, 11,
- positions of 4's are: 8, 10,
- positions of 5's are: 3, 12,
- positions of 6's are: 2,
- positions of 7's are: 6,
- positions of 8's are: 4,
- so row 7 is: 1, 9, 7, 13, 5, 11, 8, 10, 3, 12, 2, 6, 4.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10945
• Rémy Sigrist, PARI program
• Rémy Sigrist, Scatterplot of the first 832039 terms

Crossrefs

See A358090 for a similar sequence.

Cf. A000045, A001611, A342585, A356784, A358124.

Programs

PARI

See Links section.

Formula

T(n, 1) = 1.

T(n, 2) = A001611(n-1) for n > 2.