Python recursive sequence related code

Question

I am trying to make a code that produces numbers according to the following formula...

T[n] = 1 + T[n-1] * 2

numList = []
numLisst.append (1)
#Begins with a term 1.

def numSequence ():
    while True:
        for i in range (1,12):
            #Temporally set numbers from 1 to 12
            numList[i] == 1+(numList[i-1]*2)
            break
    print (numList)

numSequence()

First of all, this brings an error, list index out of index

I'd like to see this code produce the fibonacci sequences, for example,,

1, 3, 7, 15, 31, 63, 127 , ....

I hope if I use this recursive program, I would be able to find out specific order of the numbers in an array, e.g. If I'd like to find out 3rd number in the array, should be whether 7 or 15 (It would depend how I would set it)

Answer 1

One way to solve this probem (not most Pythonic implementation, though...)

# T[n] = 1 + T[n-1] * 2

def nextFibonachi(n,i):
    n = 1 + n*2
    print(str(i)+": "+str(n))
    return n,i

fibArr = []
for i in range(0,100):
    if i == 0:
        n = 0
    n,i = nextFibonachi(n, i)
    fibArr.append(n)

print(fibArr)

m = 10
print("\n"+str(m)+": "+str(fibArr[m]))

Answer 2

The recursive implementation of your formula would be the following, assuming your base case was T(1) = 1

def T(n):
    if n == 1:
        return 1
    else:
        return 1 + T(n-1)*2

Some examples

>>> [T(i) for i in range(1,10)]
[1, 3, 7, 15, 31, 63, 127, 255, 511]
>>> T(15)
32767