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A336130 Number of ways to split a strict composition of n into contiguous subsequences all having the same sum.

%I A336130 #11 Feb 15 2024 01:15:02
%S A336130 1,1,1,3,3,5,15,13,23,27,73,65,129,133,241,375,519,617,1047,1177,1859,
%T A336130 2871,3913,4757,7653,8761,13273,16155,28803,30461,50727,55741,87743,
%U A336130 100707,152233,168425,308937,315973,500257,571743,871335,958265,1511583,1621273,2449259,3095511,4335385,4957877,7554717,8407537,12325993,14301411,20348691,22896077,33647199,40267141,56412983,66090291,93371665,106615841,155161833
%N A336130 Number of ways to split a strict composition of n into contiguous subsequences all having the same sum.
%H A336130 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 A336130 The a(1) = 1 through a(7) = 13 splits:
%e A336130   (1)  (2)  (3)    (4)    (5)    (6)        (7)
%e A336130             (1,2)  (1,3)  (1,4)  (1,5)      (1,6)
%e A336130             (2,1)  (3,1)  (2,3)  (2,4)      (2,5)
%e A336130                           (3,2)  (4,2)      (3,4)
%e A336130                           (4,1)  (5,1)      (4,3)
%e A336130                                  (1,2,3)    (5,2)
%e A336130                                  (1,3,2)    (6,1)
%e A336130                                  (2,1,3)    (1,2,4)
%e A336130                                  (2,3,1)    (1,4,2)
%e A336130                                  (3,1,2)    (2,1,4)
%e A336130                                  (3,2,1)    (2,4,1)
%e A336130                                  (1,2),(3)  (4,1,2)
%e A336130                                  (2,1),(3)  (4,2,1)
%e A336130                                  (3),(1,2)
%e A336130                                  (3),(2,1)
%t A336130 splits[dom_]:=Append[Join@@Table[Prepend[#,Take[dom,i]]&/@splits[Drop[dom,i]],{i,Length[dom]-1}],{dom}];
%t A336130 Table[Sum[Length[Select[splits[ctn],SameQ@@Total/@#&]],{ctn,Join@@Permutations/@Select[IntegerPartitions[n],UnsameQ@@#&]}],{n,0,15}]
%Y A336130 The version with different instead of equal sums is A336128.
%Y A336130 Starting with a non-strict composition gives A074854.
%Y A336130 Starting with a partition gives A317715.
%Y A336130 Starting with a strict partition gives A318683.
%Y A336130 Set partitions with equal block-sums are A035470.
%Y A336130 Partitions of partitions are A001970.
%Y A336130 Partitions of compositions are A075900.
%Y A336130 Compositions of compositions are A133494.
%Y A336130 Compositions of partitions are A323583.
%Y A336130 Cf. A006951, A063834, A271619, A279375, A305551, A317508, A318684, A326519, A336127, A336132, A336134, A336135.
%K A336130 nonn
%O A336130 0,4
%A A336130 _Gus Wiseman_, Jul 11 2020
%E A336130 a(31)-a(60) from _Max Alekseyev_, Feb 14 2024