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 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). 3

%I

%S 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,

%T 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,

%U 0,0,0,0,0,0,0,0,0,0,6,35,136,309,465,505,438,310,188,103,52,23

%N 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).

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

%H R. W. Robinson, <a href="/A123546/b123546.txt">Rows 0 through 14, flattened</a>

%e Triangle begins:

%e n = 0

%e k = 0 : 0

%e ************************* total (n = 0) = 0

%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

%Y Row sums give A007111. Cf. A007112, A123545.

%K nonn,tabf

%O 0,36

%A _N. J. A. Sloane_, Nov 14 2006

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Last modified December 5 21:40 EST 2022. Contains 358594 sequences. (Running on oeis4.)