A057278 Triangle T(n,k) of number of digraphs with a source and a sink on n unlabeled nodes and k arcs, k=0..n*(n-1).
1, 0, 1, 1, 0, 0, 1, 4, 4, 1, 1, 0, 0, 0, 1, 11, 31, 45, 38, 27, 13, 5, 1, 1, 0, 0, 0, 0, 1, 23, 152, 486, 992, 1419, 1641, 1485, 1152, 707, 379, 154, 61, 16, 5, 1, 1, 0, 0, 0, 0, 0, 1, 42, 517, 3194, 12174, 32860, 68423, 116168, 166164, 204867, 219906, 206993, 170922, 124088, 78809, 43860, 21209, 8951, 3242, 1043, 288, 76, 17, 5, 1, 1
Offset: 1
Examples
Triangle begins: [1], [0,1,1], [0,0,1,4,4,1,1], [0,0,0,1,11,31,45,38,27,13,5,1,1], ... The number of digraphs with a source and a sink on 3 unlabeled nodes is 11 = 1+4+4+1+1.
References
- V. Jovovic, G. Kilibarda, Enumeration of labeled initially-finally connected digraphs, Scientific review, Serbian Scientific Society, 19-20 (1996), p. 246.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..2680 (rows 1..20)
Crossrefs
Programs
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PARI
\\ See PARI link in A350794 for program code. { my(A=A057278triang(5)); for(n=1, #A, print(A[n])) } \\ Andrew Howroyd, Jan 21 2022
Extensions
Terms a(46) and beyond from Andrew Howroyd, Jan 21 2022