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

Terms

a(0) =1a(1) =0a(2) =1a(3) =1a(4) =1a(5) =4a(6) =2a(7) =9a(8) =10a(9) =17a(10) =37a(11) =41a(12) =102a(13) =136a(14) =251a(15) =450a(16) =667a(17) =1325a(18) =2011a(19) =3658a(20) =6246a(21) =10293a(22) =18686a(23) =30461a(24) =54183a(25) =92169a(26) =157438a(27) =276414a(28) =466579a(29) =818256