Logic Building/Phase 6 - Category 4: Mathematical Combinations/Program

Pell Series

Generate Pell series (0, 1, 2, 5, 12, ...).

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# Take n
n = int(input("Enter number of terms: "))

# Generate Pell series
if n <= 0:
    print("Invalid input")
elif n == 1:
    print("0")
elif n == 2:
    print("0 1")
else:
    a, b = 0, 1
    print(a, b, end=" ")
    for i in range(2, n):
        c = 2 * b + a
        print(c, end=" ")
        a, b = b, c
    print()

Output

Enter number of terms: 8
0 1 2 5 12 29 70 169

Pell series: P(n) = 2*P(n-1) + P(n-2).

Key Concepts:

Start with 0, 1
Each next = 2*previous + previous-1
Special recurrence relation

Lucas Series