Starting from a(1)=2, a(n) = A028260(1+a(n-1)) if n is even, a(n) = A026424(a(n-1)) if n is odd.

Terms

a(0) =2a(1) =6a(2) =11a(3) =25a(4) =45a(5) =94a(6) =176a(7) =361a(8) =700a(9) =1405a(10) =2752a(11) =5533a(12) =10964a(13) =22011a(14) =43839a(15) =87868a(16) =175557a(17) =351746a(18) =703243a(19) =1407705a(20) =2814709a(21) =5631461a(22) =11261009a(23) =22524901a(24) =45044446a(25) =90091251a(26) =180165450a(27) =360333977a(28) =720640449a(29) =1441293048