a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k+1).

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =0a(5) =0a(6) =1a(7) =5a(8) =15a(9) =35a(10) =70a(11) =128a(12) =226a(13) =402a(14) =735a(15) =1375a(16) =2588a(17) =4830a(18) =8882a(19) =16108a(20) =28943a(21) =51785a(22) =92573a(23) =165525a(24) =295869a(25) =528069a(26) =940259a(27) =1669725a(28) =2957941a(29) =5229953