Trying to find the recursive function for a sequence of numbers. (Python)

Question

n	F(n)
0	1
1	4
2	10
3	19
4	37
5	70
...	...
10	2062

Trying to determine the recursive function for he above sequence of numbers. Its also given that an even and an odd n are computed differently. Any help would be appreciated.

Edit: this is what I have so far:

def F(N):
    if N <= 0:
        return 1
    elif N % 2 == 0:
        return F(N-1) + (N-1) * 6
    else:
        return F(N-1) + (N) * 3

Answer 1

It could be this formula:

2ⁿ⁺¹ + _?3n/2_? ? 1

Here is JavaScript snippet that outputs the first 11 results:

function F(n) {
    return 2**(n+1) + ((3*n)>>1) - 1;
}

for (let n = 0; n <= 10; n++) {
    console.log(n, F(n));
}

Python:

def F(n):
    return 2**(n+1) + ((3*n)//2) - 1

for n in range(11):
    print(n, F(n))

Recurrence relationship

F₀ = 1
F_n = 2F_n?1 ? 3_?(n+1)/2_? + 5

function F(n) {
    if (n == 0) return 1;
    return 2*F(n-1) - 3*((n+1)>>1) + 5;
}

for (let n = 0; n <= 10; n++) {
    console.log(n, F(n));
}

Python:

def F(n):
    if n == 0:
        return 1
    return 2*F(n-1) - 3*((n+1)//2) + 5

for n in range(11):
    print(n, F(n))