a(n) = Sum_{i=0..n} binomial(i,floor(i/2)).

Terms

a(0) =1a(1) =2a(2) =4a(3) =7a(4) =13a(5) =23a(6) =43a(7) =78a(8) =148a(9) =274a(10) =526a(11) =988a(12) =1912a(13) =3628a(14) =7060a(15) =13495a(16) =26365a(17) =50675a(18) =99295a(19) =191673a(20) =376429a(21) =729145a(22) =1434577a(23) =2786655a(24) =5490811a(25) =10691111a(26) =21091711a(27) =41150011a(28) =81266611a(29) =158825371