#periodic
solution
recurrence
relation


def has_periodic_solution(coefficients, initial_conditions, period):
    sequence = initial_conditions[:]
    n = len(sequence)

    for i in range(period):
        next_term = sum(coefficients[j] * sequence[(n + i - j) % n] for j in range(n))
        sequence.append(next_term)

    for i in range(period, len(sequence)):
        if sequence[i] != sequence[i % period]:
            return False

    return True


# Example usage
coefficients = [1, -2, 1]  # Coefficients of the recurrence relation
initial_conditions = [0, 1]  # Initial conditions
period = 3  # Period length

has_periodic = has_periodic_solution(coefficients, initial_conditions, period)

if has_periodic:
    print("The recurrence relation has a periodic solution.")
else:
    print("The recurrence relation does not have a periodic solution.")
