Ordered lone-child-avoiding trees where vertices have decreasing subtree sizes.

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =2a(5) =3a(6) =6a(7) =10a(8) =19a(9) =35a(10) =68a(11) =128a(12) =253a(13) =489a(14) =981a(15) =1930a(16) =3899a(17) =7771a(18) =15858a(19) =31915a(20) =65503a(21) =133070a(22) =274631a(23) =561371a(24) =1164240a(25) =2393652a(26) =4983614a(27) =10299238a(28) =21511537a(29) =44637483