a(n) = 2*a(n-1) + 2*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) =3a(4) =7a(5) =19a(6) =49a(7) =133a(8) =357a(9) =973a(10) =2641a(11) =7209a(12) =19651a(13) =53671a(14) =146511a(15) =400231a(16) =1093127a(17) =2986359a(18) =8157999a(19) =22287743a(20) =60888843a(21) =166350531a(22) =454471539a(23) =1241636931a(24) =3392197289a(25) =9267648789a(26) =25319638485a(27) =69174520877a(28) =188988172213a(29) =516325239669