a(n) = T(n, floor(n/2)), T given by A026519.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =5a(5) =8a(6) =16a(7) =28a(8) =65a(9) =111a(10) =251a(11) =436a(12) =1016a(13) =1763a(14) =4117a(15) =7176a(16) =16913a(17) =29521a(18) =69865a(19) =122182a(20) =290455a(21) =508595a(22) =1212905a(23) =2126312a(24) =5085224a(25) =8923136a(26) =21389824a(27) =37563930a(28) =90226449a(29) =158563368