cp's OEIS Frontend

A304405 Number of partitions of n in which the sequence of the sum of the same summands is nondecreasing.

%I A304405 #19 Oct 22 2022 08:07:53
%S A304405 1,1,2,3,5,6,10,12,18,22,31,37,52,61,80,97,127,147,189,220,277,325,
%T A304405 402,469,578,665,804,933,1121,1282,1537,1754,2081,2374,2793,3179,3739,
%U A304405 4232,4923,5587,6477,7305,8445,9519,10949,12323,14110,15825,18099,20229,23005
%N A304405 Number of partitions of n in which the sequence of the sum of the same summands is nondecreasing.
%C A304405 Number of integer partitions of n with weakly decreasing run-sums, complement A357878. - _Gus Wiseman_, Oct 22 2022
%e A304405 n |                      | Sequence of the sum of the same summands
%e A304405 --+----------------------+-----------------------------------------
%e A304405 1 | 1                    | 1
%e A304405 2 | 2                    | 2
%e A304405   | 1+1                  | 2
%e A304405 3 | 3                    | 3
%e A304405   | 2+1                  | 1, 2
%e A304405   | 1+1+1                | 3
%e A304405 4 | 4                    | 4
%e A304405   | 3+1                  | 1, 3
%e A304405   | 2+2                  | 4
%e A304405   | 2+1+1                | 2, 2
%e A304405   | 1+1+1+1              | 4
%e A304405 5 | 5                    | 5
%e A304405   | 4+1                  | 1, 4
%e A304405   | 3+2                  | 2, 3
%e A304405   | 3+1+1                | 2, 3
%e A304405   | 2+2+1                | 1, 4
%e A304405   | 1+1+1+1+1            | 5
%e A304405 6 | 6                    | 6
%e A304405   | 5+1                  | 1, 5
%e A304405   | 4+2                  | 2, 4
%e A304405   | 4+1+1                | 2, 4
%e A304405   | 3+3                  | 6
%e A304405   | 3+2+1                | 1, 2, 3
%e A304405   | 3+1+1+1              | 3, 3
%e A304405   | 2+2+2                | 6
%e A304405   | 2+2+1+1              | 2, 4
%e A304405   | 1+1+1+1+1+1          | 6
%t A304405 Table[Length[Select[IntegerPartitions[n],GreaterEqual@@Total/@Split[#]&]],{n,0,30}] (* _Gus Wiseman_, Oct 22 2022 *)
%Y A304405 The strict opposite version is A304430, ranked by A357864.
%Y A304405 The strict version is A304428, ranked by A357862.
%Y A304405 The opposite version is A304406, ranked by A357861.
%Y A304405 Number of rows in A354584 summing to n that are strictly increasing.
%Y A304405 These partitions are ranked by A357875.
%Y A304405 A000041 counts integer partitions, strict A000009.
%Y A304405 A304442 counts partitions with equal run-sums, distinct A353837.
%Y A304405 Cf. A047966, A087980, A098859, A100883, A239312, A275870, A353832, A353864.
%K A304405 nonn
%O A304405 0,3
%A A304405 _Seiichi Manyama_, May 12 2018