Question

If a(n)=24 which recursive formula could represent the sequence below?
...,24,88,664,8408,...

Answer 1

24= 3*2^3
88= 11*2^3
664= 83*2^3 -> 83=11+72 = 11 + 2^3*3^2
664=2^3 (11+2^3*3^2) = 88 +(2^3*2^3*3^2) = 88 +(24^2)

8408= 1051 * 2^3 -> 1051= 83+968 -> 968 = 2^3 * 11^2
8408= 2^3 (83+2^3*11^2) = 664 +(2^3*2^3*11^2) = 664 +(88^2)

So:
a(n) = a(n-1) + a(n-2)^2

Lets check: 88+24^2= 664
664+88^2= 8408