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A308355 Limiting row sequence of the array A128628. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A104324 A193212 A131818

Adjacent sequences:  A308352 A308353 A308354 * A308356 A308357 A308358

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 24 2019

STATUS

approved

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Last modified February 27 09:24 EST 2020. Contains 332301 sequences. (Running on oeis4.)