a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(n-1,n-3*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =3a(4) =12a(5) =30a(6) =81a(7) =273a(8) =924a(9) =2937a(10) =9270a(11) =29997a(12) =98121a(13) =319995a(14) =1042587a(15) =3409113a(16) =11184348a(17) =36746214a(18) =120852423a(19) =398010195a(20) =1312640802a(21) =4334090274a(22) =14324257167a(23) =47385596337a(24) =156892453737a(25) =519884783805