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A308355 Limiting row sequence of the array A128628. 3

%I

%S 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,

%T 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,

%U 3,3,4,3,4,5,3,4,4,5,6,4,4,5,5,6,7,4

%N Limiting row sequence of the array A128628.

%C 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.

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

%C 2

%C 2, 3

%C 2, 3, 4

%C 2, 3, 3, 4, 5

%C 2, 3, 3, 4, 4, 5, 6

%C 2, 3, 3, 4, 3, 4, 5, 4, 5, 6, 7

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

%H Clark Kimberling, <a href="/A308355/b308355.txt">Table of n, a(n) for n = 1..2000</a>

%e 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):

%e 1

%e 1 2

%e 1 2 3

%e 1 2 2 3 4

%e 1 2 2 3 3 4 5

%e 1 2 2 3 2 3 4 3 4 5 6

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

%Y Cf. A000041, A025065, A128628.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, May 24 2019

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Last modified March 30 10:31 EDT 2020. Contains 333125 sequences. (Running on oeis4.)