Initial data commit

Task/Partition-function-P/FreeBASIC/partition-function-p-1.basic

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+Function PartitionsP(n As UInteger) As ULongInt
+    ' if n > 416, the result becomes to large for a unsigned 64bit integer
+    Dim As ULongInt p(n)
+    Dim As UInteger k, j
+
+    p(0) = 1
+    For i As UInteger = 1 To n
+        k = 0
+        While TRUE
+            k += 1
+            j = (k * (3*k - 1)) \ 2
+            If (j > i) Then Exit While
+            If (k And 1) Then
+                p(i) += p(i - j)
+            Else
+                p(i) -= p(i - j)
+            End If
+            'j = (k * (3*k + 1)) \ 2
+            j += k
+            If (j > i) Then Exit While
+            If (k And 1) Then
+                p(i) += p(i - j)
+            Else
+                p(i) -= p(i - j)
+            End If
+        Wend
+    Next i
+    Return p(n)
+End Function
+
+Print !"\nPartitionsP: ";
+For x As UInteger = 0 To 12
+    Print PartitionsP(x);"  ";
+Next x
+
+Print !"\n\ndone"
+Sleep