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

Terms

a(0) =1a(1) =0a(2) =-1a(3) =2a(4) =12a(5) =26a(6) =45a(7) =109a(8) =337a(9) =957a(10) =2445a(11) =6145a(12) =15990a(13) =42435a(14) =111925a(15) =292353a(16) =762550a(17) =1995297a(18) =5230106a(19) =13701786a(20) =35864306a(21) =93862475a(22) =245723119a(23) =643381907a(24) =1684497627a(25) =4409989581a(26) =11545153305a(27) =30225470334a(28) =79132089737a(29) =207171630917