login
Triangle read by rows: T(n,k) (n>=1, 2<=k<=n+1) = number of graphs with n edges, no isolated nodes, and k nodes in largest connected component.
0

%I #9 Mar 19 2017 11:55:45

%S 1,1,1,1,2,2,1,3,4,3,1,4,7,8,6,1,6,15,16,19,11,1,7,24,34,44,44,23,1,9,

%T 38,71,97,122,112,47,1,11,61,133,211,295,371,287,106,1,13,90,249,457,

%U 659,1015,1131,763,235

%N Triangle read by rows: T(n,k) (n>=1, 2<=k<=n+1) = number of graphs with n edges, no isolated nodes, and k nodes in largest connected component.

%H Peter Steinbach, <a href="/A000664/a000664_1.pdf">Field Guide to Simple Graphs, Volume 4</a>, Part 1 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)

%e Triangle begins:

%e 1,

%e 1,1,

%e 1,2,2,

%e 1,3,4,3,

%e 1,4,7,8,6,

%e 1,6,15,16,19,11,

%e 1,7,24,34,44,44,23,

%e 1,9,38,71,97,122,112,47,

%e 1,11,61,133,211,295,371,287,106,

%e 1,13,90,249,457,659,1015,1131,763,235,

%e ...

%Y Row sums are A000664.

%K nonn,tabl

%O 1,5

%A _N. J. A. Sloane_, Mar 18 2017