A283755 Irregular triangular array read by rows: T(n,k) = number of non-isomorphic unlabeled connected graphs with loops on n nodes and with k edges.

1, 1, 1, 1, 1, 1, 3, 3, 2, 1, 2, 6, 11, 13, 10, 5, 2, 1, 3, 14, 35, 61, 75, 68, 49, 28, 13, 5, 2, 1, 6, 33, 112, 262, 463, 625, 684, 620, 468, 301, 170, 82, 35, 14, 5, 2, 1, 11, 81, 347, 1059, 2458, 4565, 7018, 9122, 10186, 9878, 8366, 6219, 4085, 2377, 1232, 582, 251, 98, 37, 14, 5, 2, 1, 23, 204, 1085, 4091, 12014, 28779, 58162, 101315, 154484, 208321, 250120, 268649, 258994

Offset: 1

Author

Marko Riedel, Mar 15 2017

Keywords

• nonn
• tabf

Comments

The range for the subindex k is from n-1 to n(n+1)/2.

Examples

			First rows are:
1,  1;
1,  1,  1;
1,  3,  3,  2,  1;
2,  6, 11, 13, 10,  5,  2,  1;
3, 14, 35, 61, 75, 68, 49, 28, 13, 5, 2, 1;
		

References

• E. Palmer and F. Harary, Graphical Enumeration, Academic Press, 1973.

Links

• Marko R. Riedel, Number of distinct connected digraphs
• Marko Riedel, Maple code for A070166 and A283755.

Crossrefs

Row sums are A054921.

Cf. A000666, A070166, A322114.

Formula

T(n,k) = A322114(k,n). - Andrew Howroyd, Oct 23 2019