a(n) = (A269590(n)^2 + 4)/5^n, n >= 0.

Terms

a(0) =4a(1) =4a(2) =8a(3) =104a(4) =212a(5) =313a(6) =11645a(7) =2329a(8) =73757a(9) =160772a(10) =646925a(11) =129385a(12) =25877a(13) =49838696a(14) =2503218301a(15) =16177487972a(16) =18226737365a(17) =3645347473