A057275 Triangle T(n,k) of number of unilaterally connected digraphs on n labeled nodes and with k arcs, k=0..n*(n-1).
1, 0, 2, 1, 0, 0, 6, 20, 15, 6, 1, 0, 0, 0, 24, 222, 660, 908, 792, 495, 220, 66, 12, 1, 0, 0, 0, 0, 120, 2304, 15540, 52700, 109545, 161120, 182946, 167660, 125945, 77520, 38760, 15504, 4845, 1140, 190, 20, 1
Offset: 1
Examples
Triangle begins: [1], [0,2,1], [0,0,6,20,15,6,1], [0,0,0,0,24,222,660,908,792,495,220,66,12,1], ... The number of unilaterally connected digraphs on 3 labeled nodes is 48 = 6+20+15+6+1.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..2680
- V. Jovovic and G. Kilibarda, Enumeration of labeled quasi-initially connected digraphs, Discrete Math., 224 (2000), 151-163.
Crossrefs
Programs
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PARI
\\ See A057273 for Strong. Unilaterally(n, e=2)={my(u=vector(n), s=Strong(n,e)); for(n=1, #u, u[n]=vector(n, k, binomial(n,k)*s[k]*if(k==n, 1, sum(j=1, n-k, e^(k*(n-k-j))*(e^(k*j)-1)*u[n-k][j])))); vector(#u, n, vecsum(u[n]))} row(n)={Vecrev(Unilaterally(n, 1+'y)[n])} { for(n=1, 5, print(row(n))) } \\ Andrew Howroyd, Jan 19 2022