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"""
[0, 1, 2, 2, 4, 6, 8, 9, -31] generates [1, 2, 3, 4, 6, 8, 10, 12, 15] as a Fibonacci sequence
sum([0, 1, 2, 2, 4, 6, 8, 9, -31]) = 1
sum([1, 2, 2, 4, 6, 8, 9, -31, 1]) = 2
sum([2, 2, 4, 6, 8, 9, -31, 1, 2]) = 3
sum([2, 4, 6, 8, 9, -31, 1, 2, 3]) = 4
sum([4, 6, 8, 9, -31, 1, 2, 3, 4]) = 6
sum([6, 8, 9, -31, 1, 2, 3, 4, 6]) = 8
sum([8, 9, -31, 1, 2, 3, 4, 6, 8]) = 10
sum([9, -31, 1, 2, 3, 4, 6, 8, 10]) = 12
sum([-31, 1, 2, 3, 4, 6, 8, 10, 12]) = 15
sum([1, 2, 3, 4, 6, 8, 10, 12, 15]) = 61
sum([2, 3, 4, 6, 8, 10, 12, 15, 61]) = 121
sum([3, 4, 6, 8, 10, 12, 15, 61, 121]) = 240
sum([4, 6, 8, 10, 12, 15, 61, 121, 240]) = 477
sum([6, 8, 10, 12, 15, 61, 121, 240, 477]) = 950
sum([8, 10, 12, 15, 61, 121, 240, 477, 950]) = 1894
sum([10, 12, 15, 61, 121, 240, 477, 950, 1894]) = 3780
sum([12, 15, 61, 121, 240, 477, 950, 1894, 3780]) = 7550
sum([15, 61, 121, 240, 477, 950, 1894, 3780, 7550]) = 15088
sum([61, 121, 240, 477, 950, 1894, 3780, 7550, 15088]) = 30161
sum([121, 240, 477, 950, 1894, 3780, 7550, 15088, 30161]) = 60261
"""
os = [1, 2, 3, 4, 6, 8, 10, 12, 15]
s = os
for i in range(0, len(os)):
s = [s[-i-1] - sum(s[0:-i-1])] + s
seed = s[0:len(os)]
print(seed, "generates", os, "as a Fibonacci sequence")
for i in range(0, 20):
term = sum(seed)
print(f"sum({seed}) = ", term)
seed = seed[1:] + [term]
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