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

Terms

a(0) =0a(1) =3a(2) =4a(3) =9a(4) =16a(5) =30a(6) =54a(7) =97a(8) =172a(9) =303a(10) =530a(11) =922a(12) =1596a(13) =2751a(14) =4724a(15) =8085a(16) =13796a(17) =23478a(18) =39858a(19) =67517a(20) =114140a(21) =192603a(22) =324454a(23) =545714a(24) =916536a(25) =1537275a(26) =2575204a(27) =4308897a(28) =7201912a(29) =12025038