This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A308355 #7 Jun 03 2019 19:47:25 %S A308355 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 A308355 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 A308355 3,3,4,3,4,5,3,4,4,5,6,4,4,5,5,6,7,4 %N A308355 Limiting row sequence of the array A128628. %C A308355 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 A308355 Beginning with the 2nd term, the sequence is a concatenation of segments that begin with 2: %C A308355 2 %C A308355 2, 3 %C A308355 2, 3, 4 %C A308355 2, 3, 3, 4, 5 %C A308355 2, 3, 3, 4, 4, 5, 6 %C A308355 2, 3, 3, 4, 3, 4, 5, 4, 5, 6, 7 %C A308355 2, 3, 3, 4, 3, 4, 5, 4, 4, 5, 6, 5, 6, 7, 8 %H A308355 Clark Kimberling, <a href="/A308355/b308355.txt">Table of n, a(n) for n = 1..2000</a> %e A308355 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 A308355 1 %e A308355 1 2 %e A308355 1 2 3 %e A308355 1 2 2 3 4 %e A308355 1 2 2 3 3 4 5 %e A308355 1 2 2 3 2 3 4 3 4 5 6 %t A308355 Take[Map[Length, IntegerPartitions[50]], 1000] %Y A308355 Cf. A000041, A025065, A128628. %K A308355 nonn,easy %O A308355 1,2 %A A308355 _Clark Kimberling_, May 24 2019