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A350609
Triangle read by rows: T(n,k) (n >= 1, 1 <= k <= n) = number of subdigraphs of the transitive tournament on n nodes that have k weak components.
4
1, 1, 1, 4, 2, 2, 31, 15, 10, 8, 474, 228, 162, 96, 64, 14357, 7057, 5242, 3296, 1792, 1024, 865024, 438662, 342394, 222720, 130048, 65536, 32768, 103931595, 54542867, 44669602, 30110848, 18337792, 10027008, 4718592, 2097152, 24935913222, 13548525896, 11608243634, 8093078016, 5130403840, 2945449984, 1518338048, 671088640, 268435456
OFFSET
1,4
COMMENTS
The sum of row n is 2^(n*(n-1)/2) = A006125(n).
For references and links see A350608.
LINKS
EXAMPLE
For example, the entries for n=3 are {4,2,2}, because the empty subgraph and the subgraphs with a single arc have 1 weak component {123}; 1->2,1->3 and 1->3,2->3 have 2 weak components (namely {1,23} and {12,3}); finally 1->2,2->3 and 1->2,1->3,2->3 have 3 weak components (namely {1,2,3}).
Triangle T(n,k) begins:
1;
1, 1;
4, 2, 2;
31, 15, 10, 8;
474, 228, 162, 96, 64;
14357, 7057, 5242, 3296, 1792, 1024;
865024, 438662, 342394, 222720, 130048, 65536, 32768;
...
CROSSREFS
Column k=1 gives A350608.
Main diagonal gives A006125(n-1).
Cf. A350610.
Sequence in context: A199221 A096870 A350149 * A261253 A328334 A359060
KEYWORD
nonn,tabl
AUTHOR
Don Knuth, Jan 16 2022
STATUS
approved