A333157
Triangle read by rows: T(n,k) is the number of n X n symmetric binary matrices with k ones in every row and column.
Original entry on oeis.org
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 10, 18, 10, 1, 1, 26, 112, 112, 26, 1, 1, 76, 820, 1760, 820, 76, 1, 1, 232, 6912, 35150, 35150, 6912, 232, 1, 1, 764, 66178, 848932, 1944530, 848932, 66178, 764, 1, 1, 2620, 708256, 24243520, 133948836, 133948836, 24243520, 708256, 2620, 1
Offset: 0
Triangle begins:
1,
1, 1;
1, 2, 1;
1, 4, 4, 1;
1, 10, 18, 10, 1;
1, 26, 112, 112, 26, 1;
1, 76, 820, 1760, 820, 76, 1;
1, 232, 6912, 35150, 35150, 6912, 232, 1;
1, 764, 66178, 848932, 1944530, 848932, 66178, 764, 1;
...
-
\\ See script in A295193 for comments.
GraphsByDegreeSeq(n, limit, ok)={
local(M=Map(Mat([x^0,1])));
my(acc(p,v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));
my(recurse(r,p,i,q,v,e) = if(e<=limit && poldegree(q)<=limit, if(i<0, if(ok(x^e+q, r), acc(x^e+q, v)), my(t=polcoeff(p,i)); for(k=0,t,self()(r,p,i-1,(t-k+x*k)*x^i+q,binomial(t,k)*v,e+k)))));
for(k=2, n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], my(p=src[i,1]); recurse(n-k, p, poldegree(p), 0, src[i,2], 0))); Mat(M);
}
Row(n)={my(M=GraphsByDegreeSeq(n, n\2, (p,r)->poldegree(p)-valuation(p,x) <= r + 1), v=vector(n+1)); for(i=1, matsize(M)[1], my(p=M[i,1], d=poldegree(p)); v[1+d]+=M[i,2]; if(pollead(p)==n, v[2+d]+=M[i,2])); for(i=1, #v\2, v[#v+1-i]=v[i]); v}
for(n=0, 8, print(Row(n))) \\ Andrew Howroyd, Mar 14 2020
A139670
Number of n X n symmetric binary matrices with all row sums 4.
Original entry on oeis.org
1, 26, 820, 35150, 1944530, 133948836, 11234051976, 1127512146540, 133475706272700, 18406586045919060, 2925154024273348296, 530686776655470875076, 109004840145995702773410, 25164525076896596670014400, 6486836210471246515195539840, 1856264107759263993451053077856
Offset: 4
a(4) = 1:
1 1 1 1
1 1 1 1
1 1 1 1
1 1 1 1
A139671
Number of n X n symmetric binary matrices with all row sums 5.
Original entry on oeis.org
1, 76, 6912, 848932, 133948836, 26615510712, 6549149852112, 1966499966796816, 711040444591249476, 305907023641901084832, 154921887640109512226304, 91469751377953081098144816, 62419855497729620428436222688, 48849705066296300911892229634944
Offset: 5
A139673
Number of n X n symmetric binary matrices with all row sums 6.
Original entry on oeis.org
1, 232, 66178, 24243520, 11234051976, 6549149852112, 4762109992158288, 4274712091685443584, 4686484162304929219950, 6209619146419137708859600, 9845751579221258486943505348, 18509102695712474753650903363840, 40904306737052771732376660591663712
Offset: 6
A139674
Number of n X n symmetric binary matrices with all row sums 7.
Original entry on oeis.org
1, 764, 708256, 805036704, 1127512146540, 1966499966796816, 4274712091685443584, 11528251571501588791296, 38295413179145036856212700, 155411811543624388078758718000, 763997249847515085736557734880512, 4511824317564827934662170498445281792
Offset: 7
A139675
Number of n X n symmetric binary matrices with all row sums 8.
Original entry on oeis.org
1, 2620, 8372754, 30649435140, 133475706272700, 711040444591249476, 4686484162304929219950, 38295413179145036856212700, 386860001875783390762182911250, 4805622573099374975572752075805000, 72929153106385401417284439399165879652
Offset: 8
Showing 1-6 of 6 results.
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