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

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =10a(5) =37a(6) =102a(7) =251a(8) =667a(9) =2011a(10) =6246a(11) =18686a(12) =54183a(13) =157438a(14) =466579a(15) =1400509a(16) =4202829a(17) =12556360a(18) =37480728a(19) =112227269a(20) =337221408a(21) =1014992763a(22) =3055963443a(23) =9203918219a(24) =27745375212a(25) =83736861040a(26) =252968402935a(27) =764733200716