Template:Gender of Boolean functions/triangles/female

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This triangle shows the numbers of female Boolean functions with arity $n$ and valency $k$. The right diagonal is ${\boldsymbol {d}}={\boldsymbol {p}}-{\boldsymbol {q}}$ = 1, 0, 2, 90, 31826, 2147158386... (compare  A007537) This is Pascal's triangle with column $k$ multiplied by ${\boldsymbol {d}}(k)$. The row sums are  A246537. k n 0 1 2 3 4 5 sums 0 1 · 1 1 1 1 1 · 1 1 1 · 0 0 1 2 1 · 1 1 2 · 0 0 1 · 2 2 3 3 1 · 1 1 3 · 0 0 3 · 2 6 1 · 90 90 97 4 1 · 1 1 4 · 0 0 6 · 2 12 4 · 90 360 1 · 31826 31826 32199 5 1 · 1 1 5 · 0 0 10 · 2 20 10 · 90 900 5 · 31826 159130 1 · 2147158386 2147158386 2147318437