OFFSET
0,7
COMMENTS
The minimum vertex-degree of the empty graph is infinity. It has been included here under k = 0. - Andrew Howroyd, Mar 09 2020
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..230 (rows n = 0..20)
EXAMPLE
Triangle begins:
1
1 0
1 1 0
4 3 1 0
23 31 9 1 0
256 515 227 25 1 0
5319 15381 10210 1782 75 1 0
MATHEMATICA
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], k==If[#=={}||Union@@#!=Range[n], 0, Min@@Length/@Split[Sort[Join@@#]]]&]], {n, 0, 5}, {k, 0, n}]
PROG
(PARI)
GraphsByMaxDegree(n)={
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(merge(r, p, v)=acc(p + sum(i=1, poldegree(p)-r-1, polcoef(p, i)*(1-x^i)), v));
my(recurse(r, p, i, q, v, e)=if(i<0, merge(r, x^e+q, v), my(t=polcoef(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)={if(n==0, [1], my(M=GraphsByMaxDegree(n), u=vector(n+1)); for(i=1, matsize(M)[1], u[n-poldegree(M[i, 1])]+=M[i, 2]); u)}
{ for(n=0, 8, print(Row(n))) } \\ Andrew Howroyd, Mar 09 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Sep 04 2019
EXTENSIONS
Terms a(28) and beyond from Andrew Howroyd, Sep 09 2019
STATUS
approved