A308355 Limiting row sequence of the array A128628.

1, 2, 2, 3, 2, 3, 4, 2, 3, 3, 4, 5, 2, 3, 3, 4, 4, 5, 6, 2, 3, 3, 4, 3, 4, 5, 4, 5, 6, 7, 2, 3, 3, 4, 3, 4, 5, 4, 4, 5, 6, 5, 6, 7, 8, 2, 3, 3, 4, 3, 4, 5, 3, 4, 4, 5, 6, 4, 5, 5, 6, 7, 5, 6, 7, 8, 9, 2, 3, 3, 4, 3, 4, 5, 3, 4, 4, 5, 6, 4, 4, 5, 5, 6, 7, 4

Offset: 1

Author

Clark Kimberling, May 24 2019

Keywords

• nonn
• easy

Comments

Conjecture: The length of maximal initial segment of this sequence that is identical to row n of A128628 is A025065(n+1), for n >= 1.

Beginning with the 2nd term, the sequence is a concatenation of segments that begin with 2:

2

2, 3

2, 3, 4

2, 3, 3, 4, 5

2, 3, 3, 4, 4, 5, 6

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

2, 3, 3, 4, 3, 4, 5, 4, 4, 5, 6, 5, 6, 7, 8

Examples

			Successive rows of A128628 (as in Jason Kimberley's comment: in row n, the k-th term is the number of parts in the k-th partition of n, assuming the parts of each partition are in nonincreasing order):
  1
  1   2
  1   2   3
  1   2   2   3   4
  1   2   2   3   3   4   5
  1   2   2   3   2   3   4   3   4   5   6
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000041, A025065, A128628.

Programs

Mathematica

Take[Map[Length, IntegerPartitions[50]], 1000]