%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 kth term is the number of parts in the kth 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
