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 A297626 Triangle read by rows in which row n gives a partition of n with the most subpartitions. 0

%I

%S 1,2,2,1,3,1,3,1,1,3,2,1,4,2,1,4,2,1,1,5,2,1,1,5,3,1,1,5,3,2,1,5,3,2,

%T 1,1,6,3,2,1,1,6,3,2,1,1,1,6,4,2,1,1,1,6,4,2,2,1,1,6,4,3,2,1,1,7,4,3,

%U 2,1,1,7,4,3,2,1,1,1,7,5,3,2,1,1,1,8,5,3,2,1,1,1,8,5,3,2,2,1,1,8,5,3,2,2,1,1,1,9,5,3,2,2,1,1,1,8,5,4,3,2,1,1,1,9,5,4,3,2,1,1,1,9,6,4,3,2,1,1,1,9,6,4,3,2,1,1,1,1,9,6,4,3,2,2,1,1,1,10,6,4,3,2,2,1,1,1

%N Triangle read by rows in which row n gives a partition of n with the most subpartitions.

%C A partition and its conjugate have the same number of subpartitions; in the case of ties, we take the lexicographically earliest partition.

%H Mathoverflow, <a href="https://mathoverflow.net/questions/281313/upper-bound-for-number-of-subpartitions-of-a-partition/">Upper bound for number of subpartitions of a partition</a>, posted Sep 16 2017

%e Triangle begins

%e 1

%e 2

%e 2 1

%e 3 1

%e 3 1 1

%e 3 2 1

%e 4 2 1

%e 4 2 1 1

%e 5 2 1 1

%e 5 3 1 1

%e 5 3 2 1

%e 5 3 2 1 1

%e 6 3 2 1 1

%e 6 3 2 1 1 1

%e 6 4 2 1 1 1

%e 6 4 2 2 1 1

%e 6 4 3 2 1 1

%e 7 4 3 2 1 1

%e 7 4 3 2 1 1 1

%e 7 5 3 2 1 1 1

%e 8 5 3 2 1 1 1

%e 8 5 3 2 2 1 1

%e 8 5 3 2 2 1 1 1

%e 9 5 3 2 2 1 1 1

%e 8 5 4 3 2 1 1 1

%e 9 5 4 3 2 1 1 1

%e 9 6 4 3 2 1 1 1

%e 9 6 4 3 2 1 1 1 1

%e 9 6 4 3 2 2 1 1 1

%Y Cf. A116480, A117500.

%K nonn,tabf

%O 1,2

%A _Brian Hopkins_, Jan 04 2018

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Last modified April 22 04:39 EDT 2019. Contains 322329 sequences. (Running on oeis4.)