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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
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
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2019
STATUS
approved