a(n) = 2*a(n-1) - a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =4a(5) =7a(6) =12a(7) =19a(8) =30a(9) =45a(10) =67a(11) =96a(12) =137a(13) =190a(14) =262a(15) =353a(16) =474a(17) =625a(18) =821a(19) =1062a(20) =1370a(21) =1745a(22) =2216a(23) =2783a(24) =3487a(25) =4328a(26) =5359a(27) =6580a(28) =8063a(29) =9808