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 A336131 #5 Jul 11 2020 07:38:43
%S A336131 1,1,2,6,9,20,44,74,123,231,441,681,1188,1889,3110,5448,8310,13046
%N A336131 Number of ways to split an integer partition of n into contiguous subsequences all having different sums.
%H A336131 Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%e A336131 The a(1) = 1 through a(4) = 9 splits:
%e A336131 (1) (2) (3) (4)
%e A336131 (1,1) (2,1) (2,2)
%e A336131 (1,1,1) (3,1)
%e A336131 (2),(1) (2,1,1)
%e A336131 (1),(1,1) (3),(1)
%e A336131 (1,1),(1) (1,1,1,1)
%e A336131 (2,1),(1)
%e A336131 (1),(1,1,1)
%e A336131 (1,1,1),(1)
%t A336131 splits[dom_]:=Append[Join@@Table[Prepend[#,Take[dom,i]]&/@splits[Drop[dom,i]],{i,Length[dom]-1}],{dom}];
%t A336131 Table[Sum[Length[Select[splits[ctn],UnsameQ@@Total/@#&]],{ctn,IntegerPartitions[n]}],{n,0,10}]
%Y A336131 The version with equal instead of different sums is A317715.
%Y A336131 Starting with a composition gives A336127.
%Y A336131 Starting with a strict composition gives A336128.
%Y A336131 Starting with a strict partition gives A336132.
%Y A336131 Partitions of partitions are A001970.
%Y A336131 Partitions of compositions are A075900.
%Y A336131 Compositions of compositions are A133494.
%Y A336131 Compositions of partitions are A323583.
%Y A336131 Cf. A006951, A063834, A279786, A305551, A316245, A323433, A336130, A336134, A336135.
%K A336131 nonn,more
%O A336131 0,3
%A A336131 _Gus Wiseman_, Jul 11 2020