binary matrices with zero diagonal & no zero rows or columns
Edwin Clark
eclark at math.usf.edu
Wed Aug 27 19:09:18 CEST 2003
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/
------------------------------------------------------------
More information about the SeqFan
mailing list