some more integer sequences to remember

tools/int_seq.py

@@ -1,5 +1,30 @@
+import math
+from functools import cache
+
+
+def factorial(n: int) -> int:
+    """
+    n! = 1 * 2 * 3 * 4 * ... * n
+    1, 1, 2, 6, 24, 120, 720, ...
+    """
+    return math.factorial(n)
+
+
+@cache
+def fibonacci(n: int) -> int:
+    """
+    F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1
+    0, 1, 1, 2, 3, 5, 8, 13, 21, ...
+    """
+    if n < 2:
+        return n
+
+    return fibonacci(n - 1) + fibonacci(n - 2)
+
+
 def triangular(n: int) -> int:
     """
+    a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n
     0, 1, 3, 6, 10, 15, ...
     """
     return int(n * (n + 1) / 2)