a(1) = 1; for n>1, a(n) = the smallest number p > a(n-1) such that (a(n-1)+p)/2 is a cube.

Terms

a(0) =1a(1) =15a(2) =39a(3) =89a(4) =161a(5) =271a(6) =415a(7) =609a(8) =849a(9) =1151a(10) =1511a(11) =1945a(12) =2449a(13) =3039a(14) =3711a(15) =4481a(16) =5345a(17) =6319a(18) =7399a(19) =8601a(20) =9921a(21) =11375a(22) =12959a(23) =14689a(24) =16561a(25) =18591a(26) =20775a(27) =23129a(28) =25649a(29) =28351