Related to number of irreducible stick-cutting problems.

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =1a(5) =1a(6) =4a(7) =7a(8) =9a(9) =21a(10) =41a(11) =73a(12) =147a(13) =288a(14) =557a(15) =1111a(16) =2193a(17) =4343a(18) =8728a(19) =17483a(20) =35063a(21) =70828a(22) =143267a(23) =290193a(24) =589705a(25) =1200646a(26) =2448904a(27) =5005001a(28) =10245216a(29) =21005238