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The formula for a 1 deep connected network is based on this formula:

⁠

[1][6][15][20][15][6]

⁠

You should notice that this is the binomial coefficient. Here’s the fully expanded output:

⁠

⁠[[ABCDE]]⁠ ⁠ ⁠[[ABCD][BCDE][CDEA][DEAB][EABC]]⁠ ⁠ ⁠[[ABC][BCD][CDE][DEA][EAB][ABC][BCD][CDE][DEA][EAB]]⁠ ⁠ ⁠[[AB][BC][CD][DE][EA][AB][BC][CD][DE][EA]]⁠ ⁠ ⁠[[A][B][C][D][E]]⁠ ⁠

⁠

⁠[]⁠ ⁠ ⁠[]⁠ ⁠ ⁠[]⁠ ⁠ ⁠[]⁠ ⁠ ⁠[]⁠ ⁠

⁠

⁠[[[1[2345]]]]⁠ ⁠ ⁠[[[1[234]]][[1[234]]][[1[234]][2[34]]][[1[234]][2[34]]][[1[234]][2[34]][3[4]]]]⁠ ⁠ ⁠[[[1[23]]][[1[23]]][[1[23]][2[3]]][[1[23]][2[3]]][[1[23]][2[3]][3[43]]][[1[23]][2[3]][3[43]]][[1[23]][2[3]][3[43]][4[543]]][[1[23]][2[3]][3[43]][4[543]]][[1[23]][2[3]][3[43]][4[543]][5[6543]]][[1[23]][2[3]][3[43]][4[543]][5[6543]]]]⁠ ⁠ ⁠[[[1[2]]][[1[2]]][[1[2]][2[32]]][[1[2]][2[32]]][[1[2]][2[32]][3[432]]][[1[2]][2[32]][3[432]]][[1[2]][2[32]][3[432]][4[5432]]][[1[2]][2[32]][3[432]][4[5432]]][[1[2]][2[32]][3[432]][4[5432]][5[65432]]][[1[2]][2[32]][3[432]][4[5432]][5[65432]]]]⁠ ⁠ ⁠[[[1[21]]][[1[21]]][[1[21]][2[321]]][[1[21]][2[321]]][[1[21]][2[321]][3[4321]]]]⁠ ⁠

⁠

[1][5][10][10][5]

⁠

You can read this as:

All the layers

The 5 ways to select 4 of the 5 elements

The 10 ways to select 3 of the 4 elements

...

The 5 ways to select 1 of each of the five elements

Sequence([Input Nodes].Count(), 1, -1).FormulaMap(WithName(CurrentValue, SequenceSize,

SequenceSize.FormulaMap(WithName(

Factorial([Input Nodes].Count())

/ (Factorial(CurrentValue) * Factorial([Input Nodes].Count() - CurrentValue)),

ComboCount,

Sequence(0, ComboCount-1).FormulaMap(WithName(CurrentValue, IndexOffset,

Sequence(0, SequenceSize-1).FormulaMap(WithName(CurrentValue, StartingIndex,

[Input Nodes].Nth(1 + Remainder(StartingIndex + IndexOffset, [Input Nodes].Count()))

))

It’s not easy to understand, but at least we have WithName providing a bit of documentation.

I don’t know how to do this without the n choose k formula (the part with all the factorials). I’m sure there’s a Monte Carlo approach, but I’m also sure this is faster.

Next thing to do is to make the formula add a row for each group. We do that with:

Sequence([Input Nodes].Count(), 1, -1).FormulaMap(WithName(CurrentValue, SequenceSize,

SequenceSize.FormulaMap(WithName(

Factorial([Input Nodes].Count())

/ (Factorial(CurrentValue) * Factorial([Input Nodes].Count() - CurrentValue)),

ComboCount,

Sequence(0, ComboCount-1).FormulaMap(WithName(CurrentValue, IndexOffset,

Norons.AddRow([DB Items].[In Edges],

Sequence(0, SequenceSize-1).FormulaMap(WithName(CurrentValue, StartingIndex,

[Input Nodes].Nth(1 + Remainder(StartingIndex + IndexOffset, [Input Nodes].Count()))

))

)

))

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