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
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