A369283 Triangle read by rows: T(n,k) is the number of labeled point-determining graphs with n nodes and k edges, n >= 0, 0 <= k <= n*(n - 1)/2.
1, 1, 0, 1, 0, 3, 0, 1, 0, 0, 3, 16, 12, 0, 1, 0, 0, 15, 60, 130, 132, 140, 80, 30, 0, 1, 0, 0, 0, 15, 600, 1692, 3160, 4635, 4620, 3480, 2088, 885, 240, 60, 0, 1, 0, 0, 0, 105, 1260, 7665, 28042, 74280, 142380, 218960, 271404, 276150, 230860, 157710, 86250, 38752, 13524, 3360, 560, 105, 0, 1
Offset: 0
Examples
Triangle begins: [0] 1; [1] 1; [2] 0, 1; [3] 0, 3, 0, 1; [4] 0, 0, 3, 16, 12, 0, 1; [5] 0, 0, 15, 60, 130, 132, 140, 80, 30, 0, 1; [6] 0, 0, 0, 15, 600, 1692, 3160, 4635, 4620, 3480, 2088, 885, 240, 60, 0, 1; ...
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1350 (rows 0..20)
- Ira M. Gessel and Ji Li, Enumeration of point-determining graphs, J. Combinatorial Theory Ser. A 118 (2011), 591-612.
Programs
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PARI
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m} edges(p,t) = {prod(i=2, #p, prod(j=1, i-1, t(p[i]*p[j])))} row(n) = {my(s=0); forpart(p=n, s += permcount(p)*(-1)^(n-#p)*edges(p, w->1 + x^w)); Vecrev(s)}
Comments