A046751 Triangle read by rows of number of connected graphs with n nodes and k edges (n >= 2, 1 <= k <= n(n-1)/2).

1, 0, 1, 1, 0, 0, 2, 2, 1, 1, 0, 0, 0, 3, 5, 5, 4, 2, 1, 1, 0, 0, 0, 0, 6, 13, 19, 22, 20, 14, 9, 5, 2, 1, 1, 0, 0, 0, 0, 0, 11, 33, 67, 107, 132, 138, 126, 95, 64, 40, 21, 10, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 23, 89, 236, 486, 814, 1169, 1454, 1579, 1515, 1290, 970, 658, 400, 220, 114

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice
• tabf

Examples

			1;
0,1,1;
0,0,2,2,1, 1;
0,0,0,3,5, 5, 4, 2,  1,  1;
0,0,0,0,6,13,19,22, 20, 14,  9,  5, 2, 1, 1;
0,0,0,0,0,11,33,67,107,132,138,126,95,64,40,21,10,5,2,1,1;
[ the 4th row giving the numbers of connected graphs with 4 nodes and from 1 to 10 edges ].
		

Links

• G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.
• Gordon Royle, Small graphs
• Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

Crossrefs

See A054924, which is the main entry for this triangle.

Cf. A002905, A008406, A046742, A054923, A054924.

Extensions

More terms from Vladeta Jovovic, Apr 21 2000