Please help me. Number 1.0.3.4.13.12.39 The general term formula of If possible, please write the derivation

Please help me. Number 1.0.3.4.13.12.39 The general term formula of If possible, please write the derivation

Let it be a U n
The questions are:
A_ 4 - A_ 2 = 4; A_ 6 -A_ 4 = 8; ==>
A_ 2*n+2 -A_ 2*n = 4*2^(n-1) ===>
A_ 2*n = 4*(2^n -1); n = 1,2,3.
A_ 3 - A_ 1 = 3 - 1 = 2 = 1+1 = 1^2 +1;
A_ 5 - A_ 3 = 13 - 3 = 10 = 9+1 = 3^2 +1;
A_ 7 - A_ 5 = 39 - 13 = 26 = 25+1 = 5^2 +1; ==>
A_ 2*n+1 - A_ 2*n-1 = (2*n - 1)^2 +1; ==>
A_ 2n+1 = n + 1 + n*(4*n^2-1)/3; n = 0,1,2.
To sum up, a_ N = 0
When n is even
When n is odd