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%I #19 Oct 22 2022 08:07:53
%S 1,1,2,3,5,6,10,12,18,22,31,37,52,61,80,97,127,147,189,220,277,325,
%T 402,469,578,665,804,933,1121,1282,1537,1754,2081,2374,2793,3179,3739,
%U 4232,4923,5587,6477,7305,8445,9519,10949,12323,14110,15825,18099,20229,23005
%N Number of partitions of n in which the sequence of the sum of the same summands is nondecreasing.
%C Number of integer partitions of n with weakly decreasing run-sums, complement A357878. - _Gus Wiseman_, Oct 22 2022
%e n | | Sequence of the sum of the same summands
%e --+----------------------+-----------------------------------------
%e 1 | 1 | 1
%e 2 | 2 | 2
%e | 1+1 | 2
%e 3 | 3 | 3
%e | 2+1 | 1, 2
%e | 1+1+1 | 3
%e 4 | 4 | 4
%e | 3+1 | 1, 3
%e | 2+2 | 4
%e | 2+1+1 | 2, 2
%e | 1+1+1+1 | 4
%e 5 | 5 | 5
%e | 4+1 | 1, 4
%e | 3+2 | 2, 3
%e | 3+1+1 | 2, 3
%e | 2+2+1 | 1, 4
%e | 1+1+1+1+1 | 5
%e 6 | 6 | 6
%e | 5+1 | 1, 5
%e | 4+2 | 2, 4
%e | 4+1+1 | 2, 4
%e | 3+3 | 6
%e | 3+2+1 | 1, 2, 3
%e | 3+1+1+1 | 3, 3
%e | 2+2+2 | 6
%e | 2+2+1+1 | 2, 4
%e | 1+1+1+1+1+1 | 6
%t Table[Length[Select[IntegerPartitions[n],GreaterEqual@@Total/@Split[#]&]],{n,0,30}] (* _Gus Wiseman_, Oct 22 2022 *)
%Y The strict opposite version is A304430, ranked by A357864.
%Y The strict version is A304428, ranked by A357862.
%Y The opposite version is A304406, ranked by A357861.
%Y Number of rows in A354584 summing to n that are strictly increasing.
%Y These partitions are ranked by A357875.
%Y A000041 counts integer partitions, strict A000009.
%Y A304442 counts partitions with equal run-sums, distinct A353837.
%Y Cf. A047966, A087980, A098859, A100883, A239312, A275870, A353832, A353864.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 12 2018
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