Q. about {0,1}-matrices.

[Ferenc Adorjan]

Hello Neil and Seqfans,

I have composed a Pari program to determine the number of nxn robust
0,1 matrices.
Certainly, the program below is neither optimal nor verfied. It
provides properly the value of 4 and 68, but as the fourth term it
gives 5440 instead of the value in your sequence (5008).
Somebody should verify the program (or the term #4) before anybody
tries to calculate the fifth term.
Ferenc

{nrobust(n)= /* # or robust nxn 0,1 matrices */
local(m,l,k,c=0);
l=2^(n^2-1);k=l-1;for(i=1,k,l++;
b=binary(l);m=matrix(n,n,x,y,b[(x-1)*n+y]);
if(robust(m),c++));return(c)
}
{sing01(m)=
local(r=1,v,k,j,s);
k=matsize(m)[1];v=vector(k);
j=1;while((r>0)&&(j<=k),v[j]=0;for(i=1,k,v[j]+=m[i,j]*2^(i-1));r=v[j];j++);
if(r==0,return(r),for(i=1,k-1,for(j=i+1,k,r=v[i]<>v[j];if(r==0,return(r)))));
j=1;while((r>0)&&(j<=k),v[j]=0;for(i=1,k,v[j]+=m[j,i]*2^(i-1));r=v[j];j++);
if(r==0,return(r),for(i=1,k-1,for(j=i+1,k,r=v[i]<>v[j];if(r==0,return(r))));return(r))
}
{robust(m)= /* it assumes that m[1,1]=1 */
local(s,j,k,n,r=1); n=matsize(m)[1];
for(i=2,n,s=matrix(i,i,x,y,m[x,y]);if(r=sing01(s),,return(r)));return(r)}