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

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =1a(6) =4a(7) =10a(8) =20a(9) =35a(10) =58a(11) =98a(12) =176a(13) =333a(14) =640a(15) =1213a(16) =2242a(17) =4052a(18) =7226a(19) =12835a(20) =22842a(21) =40788a(22) =72952a(23) =130344a(24) =232200a(25) =412190a(26) =729466a(27) =1288216a(28) =2272012a(29) =4003795