a(n) = Sum_{k=0..floor(n/2)} binomial(n,2*k)*Fibonacci(k).

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =7a(5) =15a(6) =32a(7) =70a(8) =157a(9) =357a(10) =815a(11) =1859a(12) =4232a(13) =9620a(14) =21853a(15) =49635a(16) =112747a(17) =256139a(18) =581944a(19) =1322210a(20) =3004145a(21) =6825557a(22) =15507867a(23) =35234183a(24) =80052656a(25) =181881000a(26) =413236953a(27) =938882307a(28) =2133159119a(29) =4846579847