a(n) = Sum_{k=0..floor(n/6)} (-1)^k * binomial(n-3*k,3*k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =0a(7) =-3a(8) =-9a(9) =-19a(10) =-34a(11) =-55a(12) =-82a(13) =-112a(14) =-136a(15) =-135a(16) =-75a(17) =99a(18) =469a(19) =1147a(20) =2269a(21) =3970a(22) =6325a(23) =9235a(24) =12231a(25) =14166a(26) =12771a(27) =4076a(28) =-18244a(29) =-63424