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

Terms

a(0) =1a(1) =1a(2) =1a(3) =5a(4) =21a(5) =58a(6) =149a(7) =431a(8) =1299a(9) =3784a(10) =10828a(11) =31236a(12) =90741a(13) =263178a(14) =761403a(15) =2203162a(16) =6380241a(17) =18478155a(18) =53501860a(19) =154900529a(20) =448506736a(21) =1298668192a(22) =3760269946a(23) =10887655332a(24) =31524747503a(25) =91279009255a(26) =264295580664a(27) =765258527358