|
%I #4 May 08 2019 22:20:48
%S 1,2,1,2,3,1,3,4,1,2,3,4,5,1,1,2,2,3,4,5,6,1,1,2,2,3,4,4,5,6,7,1,1,1,
%T 2,2,3,3,4,5,5,6,7,8,1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,7,8,9,1,1,1,1,1,2,
%U 2,2,2,3,3,3,3,4,4,4,5,5,6,6,7,7,8,9,10
%N Irregular triangle whose rows are the sorted combined parts of all strict integer partitions of n.
%e The strict integer partitions of 6 are {(6), (5,1), (4,2), (3,2,1)} with multiset union {1,1,2,2,3,4,5,6}, which is row n = 6.
%e Triangle begins:
%e 1
%e 2
%e 1 2 3
%e 1 3 4
%e 1 2 3 4 5
%e 1 1 2 2 3 4 5 6
%e 1 1 2 2 3 4 4 5 6 7
%e 1 1 1 2 2 3 3 4 5 5 6 7 8
%e 1 1 1 2 2 2 3 3 3 4 4 5 5 6 6 7 8 9
%t Table[Sort[Join@@Select[IntegerPartitions[n],UnsameQ@@#&]],{n,10}]
%Y Row lengths are A015723.
%Y Row sums are A066189.
%Y Row products are A325504.
%Y Run-lengths of row n are row n of A325513.
%Y Cf. A000009, A006128, A022629, A181821, A302247, A325515.
%K nonn,tabf
%O 1,2
%A _Gus Wiseman_, May 08 2019
|
