In number theory, the Padovan sequence is the sequence of integers P(n) defined by the initial values:
P(0) = P(1) = P(2) = 1
And the recurrence relation:
P(n) = P(n-2) + P(n-3)
As with any sequence defined by a recurrence relation, Padovan numbers P(m) for m<0 can be defined by rewriting the recurrence relation as:
P(m) = P(m+3) - P(m+1)
Create a function that takes two numbers, m and n, being m always negative and n always positive, and returns a list with the Padovan numbers between P(m) and P(n).
padovan(-1, 1) ➞ [0, 1, 1])
padovan(-10, 10) ➞ [2, -1, 0, 1, -1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12]
padovan(-50, 1) ➞ [-524, 245, 71, -279, 316, -208, 37, 108, -171, 145, -63, -26, 82, -89, 56, -7, -33, 49, -40, 16, 9, -24, 25, -15, 1, 10, -14, 11, -4, -3, 7, -7, 4, 0, -3, 4, -3, 1, 1, -2, 2, -1, 0, 1, -1, 1, 0, 0, 1, 0, 1, 1]
N/A