A358090 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-2 and n-1 flattened.

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

Offset

1,4

Comments

This sequence is a variant of A356784; here we consider two prior rows, there all prior rows, hence the term "partial" in the name.

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10945

Rémy Sigrist, Scatterplot of the first 832039 terms

Rémy Sigrist, PARI program

Formula

T(n, 1) = 1.

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A358120 for a similar sequence.

Cf. A000045, A001611, A342585, A356784, A358123.

Sequence in context: A209278 A326921 A370408 * A286343 A368399 A075106

Adjacent sequences: A358087 A358088 A358089 * A358091 A358092 A358093

Keyword

nonn,tabf

Author

Rémy Sigrist, Oct 30 2022

Status

approved