Initial data commit

Task/Partition-function-P/Python/partition-function-p-3.py

@@ -0,0 +1,30 @@
+from typing import List
+
+
+def partitions(n: int) -> int:
+    """Count partitions."""
+    p: List[int] = [1] + [0] * n
+    for i in range(1, n + 1):
+        k: int = 0
+        while True:
+            k += 1
+            j: int = (k * (3*k - 1)) // 2
+            if (j > i):
+                break
+            if (k & 1):
+                p[i] += p[i - j]
+            else:
+                p[i] -= p[i - j]
+            j = (k * (3*k + 1)) // 2
+            if (j > i):
+                break
+            if (k & 1):
+                p[i] += p[i - j]
+            else:
+                p[i] -= p[i - j]
+
+    return p[n]
+
+
+if __name__ == '__main__':
+    print("\nPartitions:", [partitions(x) for x in range(15)])