a(n) = Sum_{i=0..n} (C(n,i) mod 2)*Fibonacci(2*i).

Terms

a(0) =0a(1) =1a(2) =3a(3) =12a(4) =21a(5) =77a(6) =168a(7) =609a(8) =987a(9) =3572a(10) =7755a(11) =28059a(12) =47376a(13) =171409a(14) =372099a(15) =1346268a(16) =2178309a(17) =7881197a(18) =17108664a(19) =61899729a(20) =104512485a(21) =378129724a(22) =820851717a(23) =2969869413a(24) =4809706272a(25) =17401680769a(26) =37775923491a(27) =136674575148a(28) =230763520533a(29) =834910260653