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A324244 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with k peripheral nodes.

%I A324244 #21 Feb 16 2025 08:33:57
%S A324244 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 A324244 223,0,2459,1728,1523,948,405,903,3151,0,58156,36109,32119,24637,
%U A324244 13927,4713,11746,79673,0,2617378,1446609,1304109,1026845,723871,353620,110734,279535,3853870
%N A324244 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with k peripheral nodes.
%C A324244 The peripheral nodes of a graph are those with eccentricity equal to the diameter.
%H A324244 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphPeriphery.html">Graph Periphery</a>
%H A324244 Wikipedia, <a href="https://en.wikipedia.org/wiki/Distance_(graph_theory)">Distance (graph theory)</a>
%e A324244 Triangle begins:
%e A324244   1;
%e A324244   0,     1;
%e A324244   0,     1,     1;
%e A324244   0,     2,     2,     2;
%e A324244   0,     5,     4,     7,     5;
%e A324244   0,    25,    20,    16,    23,    28;
%e A324244   0,   185,   146,   119,    57,   123,  223;
%e A324244   0,  2459,  1728,  1523,   948,   405,  903,  3151;
%e A324244   0, 58156, 36109, 32119, 24637, 13927, 4713, 11746, 79673;
%e A324244   ...
%Y A324244 Row sums give A001349.
%Y A324244 Column k=2 is A324263.
%Y A324244 Rightmost diagonal is A324264.
%Y A324244 Cf. A294522, A294525, A324239.
%K A324244 nonn,tabl
%O A324244 1,8
%A A324244 _Andrew Howroyd_, Sep 02 2019