A123546 Triangle read by rows: T(n,k) = number of unlabeled graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 5, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 30, 34, 29, 17, 9, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 35, 136, 309, 465, 505, 438, 310, 188, 103, 52, 23

Offset: 0

Author

N. J. A. Sloane, Nov 14 2006

Keywords

• nonn
• tabf

Examples

			Triangle begins:
n = 0
k = 0 : 0
************************* total (n = 0) = 0
n = 1
k = 0 : 0
************************* total (n = 1) = 0
n = 2
k = 0 : 0
k = 1 : 0
************************* total (n = 2) = 0
n = 3
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
************************* total (n = 3) = 0
n = 4
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 1
************************* total (n = 4) = 1
n = 5
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 0
k = 7 : 0
k = 8 : 1
k = 9 : 1
k = 10 : 1
************************* total (n = 5) = 3
		

References

• R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

Links

• R. W. Robinson, Rows 0 through 14, flattened

Crossrefs

Row sums give A007111. Cf. A007112, A123545.