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

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =0a(7) =1a(8) =6a(9) =21a(10) =56a(11) =126a(12) =254a(13) =480a(14) =882a(15) =1617a(16) =2992a(17) =5580a(18) =10410a(19) =19292a(20) =35400a(21) =64343a(22) =116128a(23) =208701a(24) =374226a(25) =670095a(26) =1198164a(27) =2138423a(28) =3808148a(29) =6766089