a(n) = T(n, floor(n/2)), T given by A026736.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =11a(6) =21a(7) =43a(8) =79a(9) =173a(10) =309a(11) =707a(12) =1237a(13) =2917a(14) =5026a(15) =12111a(16) =20626a(17) =50503a(18) =85242a(19) =211263a(20) =354080a(21) =885831a(22) =1476368a(23) =3720995a(24) =6173634a(25) =15652239a(26) =25873744a(27) =65913927a(28) =108628550a(29) =277822147