Topic
1. Sum of Squares2. Sum of Cubes3. Alternating Sum4. Harmonic Series Sum5. Geometric Series Sum6. Print Nth Row of Pascal Triangle7. Catalan Numbers8. Tribonacci Series9. Lucas Series10. Pell Series

Pell Series

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

AdvancedPhase 6 - Category 4: Mathematical CombinationsExample 10 of 10
pell-series.py
1# Take n
2n = int(input("Enter number of terms: "))
3

4# Generate Pell series
5if n <= 0:
6    print("Invalid input")
7elif n == 1:
8    print("0")
9elif n == 2:
10    print("0 1")
11else:
12    a, b = 0, 1
13    print(a, b, end=" ")
14    for i in range(2, n):
15        c = 2 * b + a
16        print(c, end=" ")
17        a, b = b, c
18    print()

Output

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

What's going on

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

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PreviousLucas Series