login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A336131 Number of ways to split an integer partition of n into contiguous subsequences all having different sums. 12

%I #5 Jul 11 2020 07:38:43

%S 1,1,2,6,9,20,44,74,123,231,441,681,1188,1889,3110,5448,8310,13046

%N Number of ways to split an integer partition of n into contiguous subsequences all having different sums.

%H 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 The a(1) = 1 through a(4) = 9 splits:

%e (1) (2) (3) (4)

%e (1,1) (2,1) (2,2)

%e (1,1,1) (3,1)

%e (2),(1) (2,1,1)

%e (1),(1,1) (3),(1)

%e (1,1),(1) (1,1,1,1)

%e (2,1),(1)

%e (1),(1,1,1)

%e (1,1,1),(1)

%t splits[dom_]:=Append[Join@@Table[Prepend[#,Take[dom,i]]&/@splits[Drop[dom,i]],{i,Length[dom]-1}],{dom}];

%t Table[Sum[Length[Select[splits[ctn],UnsameQ@@Total/@#&]],{ctn,IntegerPartitions[n]}],{n,0,10}]

%Y The version with equal instead of different sums is A317715.

%Y Starting with a composition gives A336127.

%Y Starting with a strict composition gives A336128.

%Y Starting with a strict partition gives A336132.

%Y Partitions of partitions are A001970.

%Y Partitions of compositions are A075900.

%Y Compositions of compositions are A133494.

%Y Compositions of partitions are A323583.

%Y Cf. A006951, A063834, A279786, A305551, A316245, A323433, A336130, A336134, A336135.

%K nonn,more

%O 0,3

%A _Gus Wiseman_, Jul 11 2020

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)