%I #17 Sep 03 2019 15:11:40

%S 1,0,1,0,1,1,0,2,2,2,0,5,4,7,5,0,25,20,16,23,28,0,185,146,119,57,123,

%T 223,0,2459,1728,1523,948,405,903,3151,0,58156,36109,32119,24637,

%U 13927,4713,11746,79673,0,2617378,1446609,1304109,1026845,723871,353620,110734,279535,3853870

%N Triangle read by rows: T(n,k) is the number of connected graphs on n nodes with k peripheral nodes.

%C The peripheral nodes of a graph are those with eccentricity equal to the diameter.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphPeriphery.html">Graph Periphery</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory)</a>

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 2, 2, 2;

%e 0, 5, 4, 7, 5;

%e 0, 25, 20, 16, 23, 28;

%e 0, 185, 146, 119, 57, 123, 223;

%e 0, 2459, 1728, 1523, 948, 405, 903, 3151;

%e 0, 58156, 36109, 32119, 24637, 13927, 4713, 11746, 79673;

%e ...

%Y Row sums give A001349.

%Y Column k=2 is A324263.

%Y Rightmost diagonal is A324264.

%Y Cf. A294522, A294525, A324239.

%K nonn,tabl

%O 1,8

%A _Andrew Howroyd_, Sep 02 2019