a(n)^2 is the smallest square containing exactly n 4's.

Terms

a(0) =2a(1) =12a(2) =38a(3) =212a(4) =2538a(5) =6888a(6) =66592a(7) =210771a(8) =2059962a(9) =6696592a(10) =21081538a(11) =209868112a(12) =664488107a(13) =3800598038a(14) =18613286762a(15) =209820981888a(16) =666669703412a(17) =666516649788