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

Author

M. F. Hasler, Oct 27 2019

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A276427, A276428, A276429, A000041.

Programs

PARI

a(n)=#A276427_row(n)

Extensions

More terms from Alois P. Heinz, Oct 28 2019