A variant of the recurrence for A001190.

Terms

a(0) =0a(1) =1a(2) =1a(3) =0a(4) =1a(5) =1a(6) =2a(7) =3a(8) =6a(9) =9a(10) =18a(11) =30a(12) =60a(13) =105a(14) =210a(15) =381a(16) =765a(17) =1425a(18) =2868a(19) =5454a(20) =11004a(21) =21210a(22) =42930a(23) =83673a(24) =169851a(25) =333843a(26) =679602a(27) =1345476a(28) =2745636a(29) =5467275