a(n) = sum of the side lengths of the minimum containing squares of all partitions of n.

Terms

a(0) =0a(1) =1a(2) =4a(3) =8a(4) =16a(5) =27a(6) =47a(7) =72a(8) =115a(9) =170a(10) =255a(11) =364a(12) =527a(13) =732a(14) =1026a(15) =1401a(16) =1916a(17) =2568a(18) =3451a(19) =4556a(20) =6023a(21) =7859a(22) =10245a(23) =13217a(24) =17041a(25) =21766a(26) =27770a(27) =35173a(28) =44471a(29) =55874