a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-3*k, n).

Terms

a(0) =1a(1) =2a(2) =6a(3) =21a(4) =75a(5) =273a(6) =1009a(7) =3770a(8) =14202a(9) =53846a(10) =205216a(11) =785460a(12) =3017106a(13) =11624580a(14) =44905518a(15) =173863965a(16) =674506059a(17) =2621371005a(18) =10203609597a(19) =39773263035a(20) =155231706951a(21) =606554343495