This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A304430 #18 Oct 22 2022 08:07:47
%S A304430 1,1,2,2,3,3,5,5,6,8,10,10,13,15,18,19,22,26,33,33,38,41,50,53,60,68,
%T A304430 77,84,94,100,116,122,136,148,172,182,206,219,246,258,281,301,341,365,
%U A304430 397,429,466,489,528,572,623,660,728,773,849,895,968,1019,1120,1188,1288
%N A304430 Number of partitions of n in which the sequence of the sum of the same summands is decreasing.
%C A304430 Number of integer partitions of n with strictly increasing run-sums. - _Gus Wiseman_, Oct 22 2022
%F A304430 a(n) <= A304406(n).
%e A304430 n | | Sequence of the sum of the same summands
%e A304430 --+----------------------+-----------------------------------------
%e A304430 1 | 1 | 1
%e A304430 2 | 2 | 2
%e A304430 | 1+1 | 2
%e A304430 3 | 3 | 3
%e A304430 | 1+1+1 | 3
%e A304430 4 | 4 | 4
%e A304430 | 2+2 | 4
%e A304430 | 1+1+1+1 | 4
%e A304430 5 | 5 | 5
%e A304430 | 2+1+1+1 | 3, 2
%e A304430 | 1+1+1+1+1 | 5
%e A304430 6 | 6 | 6
%e A304430 | 3+3 | 6
%e A304430 | 2+2+2 | 6
%e A304430 | 2+1+1+1+1 | 4, 2
%e A304430 | 1+1+1+1+1+1 | 6
%t A304430 Table[Length[Select[IntegerPartitions[n],Less@@Total/@Split[#]&]],{n,0,30}] (* _Gus Wiseman_, Oct 22 2022 *)
%Y A304430 The weak opposite version is A304405, ranked by A357875.
%Y A304430 The weak version is A304406, ranked by A357861.
%Y A304430 The opposite version is A304428, ranked by A357862.
%Y A304430 Number of rows in A354584 summing to n that are strictly decreasing.
%Y A304430 These partitions are ranked by A357864.
%Y A304430 A000041 counts integer partitions, strict A000009.
%Y A304430 A304442 counts partitions with equal run-sums, distinct A353837.
%Y A304430 Cf. A047966, A087980, A098859, A100471, A100881, A239312, A275870, A353832, A353833, A353864.
%K A304430 nonn
%O A304430 0,3
%A A304430 _Seiichi Manyama_, May 12 2018