Number of rucksack partitions of n: every consecutive constant subsequence has a different sum.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =4a(5) =6a(6) =8a(7) =11a(8) =14a(9) =19a(10) =25a(11) =33a(12) =39a(13) =51a(14) =65a(15) =82a(16) =101a(17) =126a(18) =154a(19) =191a(20) =232a(21) =284a(22) =343a(23) =416a(24) =496a(25) =600a(26) =716a(27) =855a(28) =1018a(29) =1209