#periodic







# Example usage



if __name__ == '__main__':
    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
    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.")
