A361588
Triangle read by rows: T(n,k) is the number of digraphs on n unlabeled nodes with k strongly connected components and without isolated nodes.
Original entry on oeis.org
1, 0, 0, 0, 1, 1, 0, 5, 4, 4, 0, 83, 57, 37, 25, 0, 5048, 2411, 1110, 550, 271, 0, 1047008, 325015, 101467, 37140, 15024, 5682, 0, 705422362, 136887749, 27765860, 7139149, 2259378, 780314, 237684, 0, 1580348371788, 183852357683, 23088181536, 3923330808, 907186816, 258971872, 78716548, 20042357
Offset: 0
Triangle begins:
1;
0, 0;
0, 1, 1;
0, 5, 4, 4;
0, 83, 57, 37, 25;
0, 5048, 2411, 1110, 550, 271;
0, 1047008, 325015, 101467, 37140, 15024, 5682;
...
A361586
Number of digraphs on n unlabeled nodes in which every node belongs to a directed cycle.
Original entry on oeis.org
1, 0, 1, 5, 90, 5289, 1071691, 712342075, 1585944117738, 12152982231404393, 328276896613548366675, 31834464336872565979301363, 11234630426387288679040317490771, 14576388456695908232721134339830232699, 70075904005979773819582865772534172929477101
Offset: 0
A361592
Triangular array read by rows. T(n,k) is the number of labeled digraphs on [n] with exactly k strongly connected components of size 1, n>=0, 0<=k<=n.
Original entry on oeis.org
1, 0, 1, 1, 0, 3, 18, 21, 0, 25, 1699, 1080, 774, 0, 543, 587940, 267665, 103860, 59830, 0, 29281, 750744901, 225144360, 64169325, 19791000, 10110735, 0, 3781503, 3556390155318, 672637205149, 126726655860, 29445913175, 7939815030, 3767987307, 0, 1138779265
Offset: 0
Triangle begins:
1;
0, 1;
1, 0, 3;
18, 21, 0, 25;
1699, 1080, 774, 0, 543;
587940, 267665, 103860, 59830, 0, 29281;
...
- E. de Panafieu and S. Dovgal, Symbolic method and directed graph enumeration, arXiv:1903.09454 [math.CO], 2019.
- R. W. Robinson, Counting digraphs with restrictions on the strong components, Combinatorics and Graph Theory '95 (T.-H. Ku, ed.), World Scientific, Singapore (1995), 343-354.
- Wikipedia, Strongly connected component
-
nn = 7; B[n_] := n! 2^Binomial[n, 2]; strong = Select[Import["https://oeis.org/A003030/b003030.txt", "Table"], Length@# == 2 &][[All, 2]];s[x_] := Total[strong Table[x^i/i!, {i, 1, 58}]]; ggfz[egfx_] := Normal[Series[egfx, {x, 0, nn}]] /.Table[x^i -> z^i/2^Binomial[i, 2], {i, 0, nn}];Table[Take[(Table[B[n], {n, 0, nn}] CoefficientList[Series[1/ggfz[Exp[-(s[x] - x + u x)]], {z, 0, nn}], {z,u}])[[i]], i], {i, 1, nn + 1}] // Grid
Showing 1-3 of 3 results.