Natural numbers with the maximum number of "feasible" partitions of length m.

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =7a(5) =16a(6) =18a(7) =19a(8) =22a(9) =43a(10) =46a(11) =124a(12) =367a(13) =1096a(14) =3283a(15) =9844a(16) =29527a(17) =88576a(18) =265723a(19) =797164a(20) =2391487a(21) =7174456a(22) =21523363a(23) =64570084a(24) =193710247a(25) =581130736a(26) =1743392203a(27) =5230176604