Antidiagonal sums of a triangle of coefficients of recurrences of the Fibonacci sequence.

Terms

a(0) =1a(1) =1a(2) =3a(3) =0a(4) =3a(5) =0a(6) =7a(7) =1a(8) =11a(9) =0a(10) =17a(11) =0a(12) =29a(13) =1a(14) =47a(15) =0a(16) =75a(17) =0a(18) =123a(19) =1a(20) =199a(21) =0a(22) =321a(23) =0a(24) =521a(25) =1a(26) =843a(27) =0a(28) =1363a(29) =0