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

1,2

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

Links

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

Example

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

Mathematica

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

Crossrefs

Cf. A000041, A025065, A128628.

Sequence in context: A237715 A238458 A182744 * A336346 A338283 A104324

Adjacent sequences: A308352 A308353 A308354 * A308356 A308357 A308358

Keyword

nonn,easy

Author

Clark Kimberling, May 24 2019

Status

approved