a(n) = 2^n*(n^2/4+n/4+4) - Fibonacci(n+4).

Terms

a(0) =1a(1) =4a(2) =14a(3) =43a(4) =123a(5) =334a(6) =873a(7) =2215a(8) =5488a(9) =13335a(10) =31879a(11) =75166a(12) =175141a(13) =403907a(14) =923112a(15) =2092971a(16) =4711827a(17) =10540350a(18) =23444177a(19) =51875855a(20) =114248416a(21) =250534639a(22) =547235279a(23) =1190985918a(24) =2583373453a(25) =5586298699a(26) =12045209048a(27) =25902675235a(28) =55563961083a(29) =118913382430