Strict Integer Partition UDF

[Juggler_IN]

I am trying to generate a function to compute strict integer partition count for a given n. I am referencing the below recursive code.

My recursive code is also attached which is not giving the output for a given n. The expected output is 1, 1, 1, 2, 2, 3, 4, 5, 6, 8 for n=1 to 10.

def partitionsQ(n,d=0):    
#http://mathworld.wolfram.com/PartitionFunctionQ.html
#http://reference.wolfram.com/language/ref/PartitionsQ.html
#https://oeis.org/A000009
#https://codegolf.stackexchange.com/a/71945/17547    
if n==0: return 1    
return sum(partitionsQ(n-k,n-2*k+1) for k in range(1,n-d+1))

Function partitionsQ(n, Optional d = 0)
    
    Dim k

    If n = 0 Then partitionsQ = 1
    
    For k = 1 To n - d + 1
        partitionsQ = partitionsQ + partitionsQ(n - k, n - 2 * k + 1)
    Next

End Function

 

[Juggler_IN]

To further add, the output is the coefficients of Taylor series expansion of (1x^n) ... reference - Partitions

 

[Eric W]

I'm not entirely sure of the underlying mathematics, nor is my Python good enough to be sure that the translation to VBA is correct, but this version of the UDF generates the same results as the OEIS sequence up to 20. I wouldn't take it much higher since it's a very inefficient function, and already noticeably slow at 20.

Function partitionsQ(n, Optional d = 0)
Dim k As Long

    If n = 0 Then
        partitionsQ = 1
    Else
        For k = 1 To n - d
            partitionsQ = partitionsQ + partitionsQ(n - k, n - 2 * k + 1)
        Next
    End If

End Function

 

[pgc01]

I am trying to generate a function to compute strict integer partition count for a given n. I am referencing the below recursive code.

My recursive code is also attached which is not giving the output for a given n. The expected output is 1, 1, 1, 2, 2, 3, 4, 5, 6, 8 for n=1 to 10.

Hi

I believe that's the result for n=0 to 9, not n=1 to 10

Try also:

Function PartC(n As Long, Optional i As Long = 1) As Long

For i = i To (n - 1) \ 2
    PartC = PartC + PartC(n - i, i + 1)
Next i
PartC = PartC + 1
End Function