a(n) = Sum_{i=0..floor(q(n)/3)} binomial(n-3*(i+1), q(n)-3*i) with q(n) = ceiling((n-3)/2).

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =11a(6) =21a(7) =39a(8) =75a(9) =141a(10) =273a(11) =519a(12) =1009a(13) =1933a(14) =3770a(15) =7263a(16) =14202a(17) =27479a(18) =53846a(19) =104543a(20) =205216a(21) =399543a(22) =785460a(23) =1532779a(24) =3017106a(25) =5899167a(26) =11624580a(27) =22766607a(28) =44905518a(29) =88073091