|
%I #25 Oct 21 2022 22:13:21
%S 1,1,2,2,4,3,6,5,9,8,11,11,20,16,20,21,32,30,41,38,50,48,62,64,89,81,
%T 97,100,123,123,151,154,187,183,221,221,279,272,312,316,377,376,446,
%U 460,531,547,628,641,754,746,841,856,990,1007,1145,1167,1325,1346,1519,1567,1776
%N Number of partitions of n in which the sequence of the sum of the same summands is nonincreasing.
%C Number of integer partitions of n with weakly increasing run-sums. - _Gus Wiseman_, Oct 21 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 | 1+1+1 | 3
%e 4 | 4 | 4
%e | 2+2 | 4
%e | 2+1+1 | 2, 2
%e | 1+1+1+1 | 4
%e 5 | 5 | 5
%e | 2+1+1+1 | 3, 2
%e | 1+1+1+1+1 | 5
%e 6 | 6 | 6
%e | 3+3 | 6
%e | 3+1+1+1 | 3, 3
%e | 2+2+2 | 6
%e | 2+1+1+1+1 | 4, 2
%e | 1+1+1+1+1+1 | 6
%t Table[Length[Select[IntegerPartitions[n],LessEqual@@Total/@Split[#]&]],{n,0,30}] (* _Gus Wiseman_, Oct 21 2022 *)
%Y Cf. A100882.
%Y These partitions are ranked by A357861.
%Y The complement is A357865, ranked by A357850.
%Y The opposite version is A304405, ranked by A357875.
%Y The strict version is A304430, ranked by A357864.
%Y The strict opposite version is A304428, ranked by A357862.
%Y Number of rows in A354584 summing to n that are weakly decreasing.
%Y A000041 counts integer partitions, strict A000009.
%Y A304442 counts partitions with equal run-sums, distinct A353837.
%Y Cf. A047966, A087980, A098859, A239312, A275870, A353832, A353833, A353864.
%K nonn
%O 0,3
%A _Seiichi Manyama_, May 12 2018
|
