cp's OEIS Frontend

A336127 Number of ways to split a composition of n into contiguous subsequences with different sums.

%I A336127 #8 Jul 11 2020 07:38:20
%S A336127 1,1,2,8,16,48,144,352,896,2432,7168,16896,46080,114688,303104,843776,
%T A336127 2080768,5308416,13762560,34865152,87818240,241172480,583008256,
%U A336127 1503657984,3762290688,9604956160,23689428992,60532195328,156397207552,385137770496,967978254336
%N A336127 Number of ways to split a composition of n into contiguous subsequences with different sums.
%C A336127 A composition of n is a finite sequence of positive integers summing to n.
%H A336127 Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>
%F A336127 a(n) = Sum_{k=0..n} 2^(n-k) k! A008289(n,k).
%e A336127 The a(0) = 1 through a(4) = 16 splits:
%e A336127   ()  (1)  (2)    (3)        (4)
%e A336127            (1,1)  (1,2)      (1,3)
%e A336127                   (2,1)      (2,2)
%e A336127                   (1,1,1)    (3,1)
%e A336127                   (1),(2)    (1,1,2)
%e A336127                   (2),(1)    (1,2,1)
%e A336127                   (1),(1,1)  (1),(3)
%e A336127                   (1,1),(1)  (2,1,1)
%e A336127                              (3),(1)
%e A336127                              (1,1,1,1)
%e A336127                              (1),(1,2)
%e A336127                              (1),(2,1)
%e A336127                              (1,2),(1)
%e A336127                              (2,1),(1)
%e A336127                              (1),(1,1,1)
%e A336127                              (1,1,1),(1)
%t A336127 splits[dom_]:=Append[Join@@Table[Prepend[#,Take[dom,i]]&/@splits[Drop[dom,i]],{i,Length[dom]-1}],{dom}];
%t A336127 Table[Sum[Length[Select[splits[ctn],UnsameQ@@Total/@#&]],{ctn,Join@@Permutations/@IntegerPartitions[n]}],{n,0,10}]
%Y A336127 The version with equal instead of different sums is A074854.
%Y A336127 Starting with a strict composition gives A336128.
%Y A336127 Starting with a partition gives A336131.
%Y A336127 Starting with a strict partition gives A336132
%Y A336127 Partitions of partitions are A001970.
%Y A336127 Partitions of compositions are A075900.
%Y A336127 Compositions of compositions are A133494.
%Y A336127 Compositions of partitions are A323583.
%Y A336127 Cf. A006951, A063834, A279786, A305551, A316245, A317715, A323433, A336130, A336134, A336135.
%K A336127 nonn
%O A336127 0,3
%A A336127 _Gus Wiseman_, Jul 09 2020