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

Terms

a(0) =1a(1) =1a(2) =2a(3) =8a(4) =16a(5) =48a(6) =144a(7) =352a(8) =896a(9) =2432a(10) =7168a(11) =16896a(12) =46080a(13) =114688a(14) =303104a(15) =843776a(16) =2080768a(17) =5308416a(18) =13762560a(19) =34865152a(20) =87818240a(21) =241172480a(22) =583008256a(23) =1503657984a(24) =3762290688a(25) =9604956160a(26) =23689428992a(27) =60532195328a(28) =156397207552a(29) =385137770496