binary matrices with zero diagonal & no zero rows or columns

[Edwin Clark]

Brendan,

Excellent! I thought this should be amenable to counting. I had also
calculated that a(5) = 592260. So direct calculation agrees with your
formula for the first 5 numbers. It's got to be right!

I will submit it to the OEIS and credit you with the formula.

Edwin 


On Wed, 27 Aug 2003, Brendan McKay wrote:
> 
> I scribbled down an inclusion-exclusion for this, applied the binomial
> theorem twice, and to my great amazement got perfect agreement:
> 
>   sum( f(n,r), r=0..n )   where
> 
> f(n,r)
>  = binomial(n,r) (-1)^r (1-2^(-n+r+1))^(n-r) (1-2^(-n+r))^r 2^((n-r)(n-1))
> 
> Values:
>   0, 1, 18, 1699, 592260, 754179301, 3562635108438, 63770601591579079,
>         4405870283636411477640, 1190873924687350003735546441,
>         1270602397076493907445608866890778,
>         5381240610642043789096251476993474339179 
> 
> Brendan.
> 

------------------------------------------------------------
    W. Edwin Clark, Math Dept, University of South Florida,
           http://www.math.usf.edu/~eclark/
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