a(1) = 1; a(n+1) = a(n) + (largest square <= a(n)).

Terms

a(0) =1a(1) =2a(2) =3a(3) =4a(4) =8a(5) =12a(6) =21a(7) =37a(8) =73a(9) =137a(10) =258a(11) =514a(12) =998a(13) =1959a(14) =3895a(15) =7739a(16) =15308a(17) =30437a(18) =60713a(19) =121229a(20) =242333a(21) =484397a(22) =967422a(23) =1933711a(24) =3865811a(25) =7730967a(26) =15459367a(27) =30912128a(28) =61814609a(29) =123625653