a(n) = Fibonacci(n)*(Fibonacci(n-1)^2 + Fibonacci(n+1)^2).

Terms

a(0) =0a(1) =1a(2) =5a(3) =20a(4) =87a(5) =365a(6) =1552a(7) =6565a(8) =27825a(9) =117844a(10) =499235a(11) =2114729a(12) =8958240a(13) =37947545a(14) =160748653a(15) =680941780a(16) =2884516383a(17) =12219006325a(18) =51760543280a(19) =219261176861a(20) =928805254905