A simple grammar: partial sums of A008965.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =6a(5) =11a(6) =18a(7) =31a(8) =50a(9) =85a(10) =144a(11) =251a(12) =438a(13) =789a(14) =1420a(15) =2601a(16) =4792a(17) =8907a(18) =16618a(19) =31219a(20) =58814a(21) =111301a(22) =211180a(23) =401925a(24) =766648a(25) =1465899a(26) =2808082a(27) =5389509a(28) =10360576a(29) =19948155