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%I #7 Nov 22 2020 20:22:36
%S 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,
%T 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,
%U 0,0,0,0,0,0,0,0,0,5,35,136,309,465,505,438,310,188,103,52,23
%N Triangle read by rows: T(n,k) = number of unlabeled connected graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2).
%D R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.
%H R. W. Robinson, <a href="/A123545/b123545.txt">Rows 1 through 14, flattened</a>
%e Triangle begins:
%e n = 1
%e k = 0 : 0
%e ************************ TOTAL (n = 1) = 0
%e n = 2
%e k = 0 : 0
%e k = 1 : 0
%e ************************ TOTAL (n = 2) = 0
%e n = 3
%e k = 0 : 0
%e k = 1 : 0
%e k = 2 : 0
%e k = 3 : 0
%e ************************ TOTAL (n = 3) = 0
%e n = 4
%e k = 0 : 0
%e k = 1 : 0
%e k = 2 : 0
%e k = 3 : 0
%e k = 4 : 0
%e k = 5 : 0
%e k = 6 : 1
%e ************************ TOTAL (n = 4) = 1
%e n = 5
%e k = 0 : 0
%e k = 1 : 0
%e k = 2 : 0
%e k = 3 : 0
%e k = 4 : 0
%e k = 5 : 0
%e k = 6 : 0
%e k = 7 : 0
%e k = 8 : 1
%e k = 9 : 1
%e k = 10 : 1
%e ************************ TOTAL (n = 5) = 3
%e From _Hugo Pfoertner_, Nov 22 2020: (Start)
%e Transposed table:
%e Nodes Sums
%e 4 5 6 7 8 9 10 11 12 13 |A338604
%e Edges-----------------------------------------------------|-------
%e 6 | 1 . . . . . . . . . | 1
%e 7 | . . . . . . . . . . | 0
%e 8 | . 1 . . . . . . . . | 1
%e 9 | . 1 2 . . . . . . . | 3
%e 10 | . 1 4 . . . . . . . | 5
%e 11 | . . 5 4 . . . . . . | 9
%e 12 | . . 4 18 5 . . . . . | 27
%e 13 | . . 2 30 35 . . . . . | 67
%e 14 | . . 1 34 136 27 . . . . | 198
%e 15 | . . 1 29 309 288 19 . . . | 646
%e 16 | . . . 17 465 1377 357 . . . | 2216
%e 17 | . . . 9 505 3978 3478 208 . . | 8178
%e 18 | . . . 5 438 7956 18653 4958 85 . | 32085
%e 19 | . . . 2 310 11904 65011 50575 4291 . | 132093
%e 20 | . . . 1 188 14134 163812 302854 85421 1958 | 568368
%e (End)
%Y Row sums give A007112. Cf. A123546, A338604.
%K nonn,tabf
%O 1,35
%A _N. J. A. Sloane_, Nov 13 2006
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