a(n) = (Fibonacci(6*n+1) - 1)/4.

Terms

a(0) =0a(1) =3a(2) =58a(3) =1045a(4) =18756a(5) =336567a(6) =6039454a(7) =108373609a(8) =1944685512a(9) =34895965611a(10) =626182695490