A367143 Number of simple graphs on n unlabeled vertices without isolated or universal vertices.
1, 0, 0, 0, 3, 12, 88, 732, 10258, 249976, 11455832, 994987528, 163053176864, 50171849022768, 28953151594499584, 31368377658489837792, 63938162732587949277392, 245807862122123877567929920, 1787085853417304634682510751296, 24634234097674713300981911735051072
Offset: 0
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 0..87
Programs
-
Maple
b:= proc(n, i, l) `if`(n=0 or i=1, 1/n!*2^((p-> add(ceil((p[j]-1)/2) +add(igcd(p[k], p[j]), k=1..j-1), j=1..nops(p)))([l[], 1$n])), add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)) end: a:= n-> `if`(n<2, 1-n, b(n$2, [])-2*b(n-1$2, [])): seq(a(n), n=0..20); # Alois P. Heinz, Nov 06 2023 -
Mathematica
b[n_, i_, l_] := If[n == 0 || i == 1, 1/n!*2^(Function[p, Sum[Ceiling[(p[[j]]-1)/2] + Sum[GCD[p[[k]], p[[j]]], {k, 1, j-1}], {j, 1, Length[p]}]][Join[l, Table[1, {n}]]]), Sum[b[n-i*j, i-1, Join[l, Table[i, {j}]]]/j!/i^j, {j, 0, n/i}]]; a[n_] := If[n < 2, 1-n, b[n, n, {}] - 2*b[n-1, n-1, {}]]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 02 2025, after Alois P. Heinz *)
Comments