Tribonacci Calculator

from decimal import Decimal

def tribonacci(n: int, a: int = 0, b: int = 0, c: int = 1) -> list[int]:
    """Generate the first n terms of the Tribonacci sequence."""
    if n <= 0:
        return []
    seq = [a, b, c]
    while len(seq) < n:
        seq.append(seq[-1] + seq[-2] + seq[-3])
    return seq[:n]

# Standard Tribonacci sequence
seq = tribonacci(20)
print("Tribonacci sequence (first 20 terms):")
print(seq)

# Show ratios converging to Tribonacci constant (~1.8392867552141612)
print("\nRatios (approaching Tribonacci constant):")
for i in range(5, 20):
    ratio = seq[i] / seq[i-1] if seq[i-1] != 0 else 0
    print(f"T({i})/T({i-1}) = {seq[i]}/{seq[i-1]} ≈ {ratio:.10f}")

# Custom starting values
custom = tribonacci(15, a=1, b=1, c=2)
print("\nCustom (1,1,2):", custom)