partition_num.py

def intsfrom1(): # gens ints starting at 1
    n = 1
    while True:
        yield n
        n = n + 1


def oddsfrom3(): # gens odds starting at 3
    n = 3
    while True:
        yield n
        n = n+2


def tochange(): # gens the sequence of what numbers before to add/subtract
    ints = intsfrom1()
    odds = oddsfrom3()
    current = 1
    yield current
    while True: # builds from the difference being the sequence of ints and odds
        current = current + next(ints)
        yield current
        current = current + next(odds)
        yield current


        
      
    

partiton_seq = [1] # sequene of partition numbers

end = 1000 # how many iterations before stopping, since we already have 1 term, this is the number of extra terms, so you will get up to the end+1 term in the list

for iteration in range(end): # interates through the last nth number in the list, adding and subtracting to find the next term, then appends that term to the list
    seq_len = len(partiton_seq)
    counter = 0 # counts how many added
    add = True # true when adding, false when subtracting
    next_term = 0 # variable to store the next term, generated by adding/subtracting previous values
    for n in tochange(): # tochange gives what numbers to add/subtract to find the next term, this goes through all of those numbers and adds/subtracts
        # twice, then changes, until the list is too small for the next one to add/subtract, then stops
        if n > seq_len:
            break # stops if seqence isn't long enough
        if counter == 2:
            add = not add # flips add/subtract after 2 iterations of adding/subtracting
            counter = 0
        if add:
            next_term = next_term + partiton_seq[-n] # adds the nth last in the seqence, eg: -1 is the last
        else:
            next_term = next_term - partiton_seq[-n] # subtracts the nth last in the seqence, eg: -1 is the last
        counter = counter+1 # increments the counter
    
    partiton_seq.append(next_term) # adds the next term to the sequence


print(partiton_seq[:30]) # prints the first 30 partition numbers