a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-5*k,n-3*k).

Terms

a(0) =1a(1) =2a(2) =6a(3) =19a(4) =67a(5) =242a(6) =890a(7) =3310a(8) =12423a(9) =46959a(10) =178526a(11) =681893a(12) =2614698a(13) =10059000a(14) =38807021a(15) =150080294a(16) =581649776a(17) =2258469988a(18) =8783966719a(19) =34214789901a(20) =133450049457a(21) =521134066663