a(n) = Sum_{k=0..floor(n/6)} (7*k+1) * binomial(2*n-5*k+1,n-6*k)/(2*n-5*k+1).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =14a(5) =42a(6) =133a(7) =437a(8) =1474a(9) =5070a(10) =17706a(11) =62594a(12) =223517a(13) =804931a(14) =2919732a(15) =10657195a(16) =39112905a(17) =144243948a(18) =534251361a(19) =1986419632a(20) =7411559420a(21) =27740913054a(22) =104131680951a(23) =391913404280