A328806 Row lengths of A276427: largest k such that a partition of n has k-1 distinct parts i of multiplicity i.

1, 2, 1, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7

Offset

0,2

Comments

Columns of A276427 are numbered starting with 0, so the row length is one more than the index of the last column.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20539

Formula

a(n) = A394247(n) + 1. - Alois P. Heinz, May 09 2026

Example

For n = 0, the empty partition [] has 0 parts i with multiplicity i, so a(0) = 1.
For n = 1, the partition [1] has one part i with multiplicity i, whence a(1) = 2.
For n = 2, both partitions [1,1] and [2] have 0 parts i with multiplicity i, so a(2) = 1.
For n = 3, the partition [1,2] has one part i with multiplicity i, hence a(3) = 2.
For n = 4, the partitions [1,3] and [2,2] have one part i with multiplicity i, so a(4) = 2.
For n = 5, the partition [1,2,2] has 2 parts i with multiplicity i, hence a(5) = 3.
The smallest partition with k-1 = 3 parts i with multiplicity i is [1,2,2,3,3,3], for n = 14, whence a(14) = 4.

Prog

(PARI) a(n)=#A276427_row(n)

Crossrefs

Cf. A276427, A276428, A276429, A000041, A394247.

Sequence in context: A071068 A352104 A240872 * A326370 A137735 A365576

Adjacent sequences: A328803 A328804 A328805 * A328807 A328808 A328809

Keyword

nonn

Author

M. F. Hasler, Oct 27 2019

Extensions

More terms from Alois P. Heinz, Oct 28 2019

Status

approved