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

1,3

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.

Example

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.

Prog

(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

Crossrefs

Row sums give A003029.

The unlabeled version is A057270.

Cf. A057271, A057272, A057273, A057274, A062735.

Sequence in context: A267163 A357885 A265163 * A057271 A021480 A201299

Adjacent sequences: A057272 A057273 A057274 * A057276 A057277 A057278

Keyword

nonn,tabf

Author

Vladeta Jovovic, Goran Kilibarda, Sep 14 2000

Status

approved