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%I #10 Sep 18 2018 12:15:11
%S 1,1,1,1,0,1,1,1,1,1,1,0,1,0,1,1,1,2,2,1,1,1,0,1,0,1,0,1,1,1,2,3,3,2,
%T 1,1,1,0,2,0,3,0,2,0,1,1,1,2,3,4,4,3,2,1,1,1,0,1,0,2,0,2,0,1,0,1,1,1,
%U 4,7,11,13,13,11,7,4,1,1,1,0,1,0,3,0,4,0,3,0,1,0,1
%N Triangle read by rows: T(n,k) is the number of vertex transitive graphs with n nodes and valency k, (0 <= k < n).
%H Andrew Howroyd, <a href="/A319367/b319367.txt">Table of n, a(n) for n = 1..496</a>
%H B. D. McKay and G. F. Royle, <a href="/A006799/a006799.pdf">The transitive graphs with at most 26 vertices</a>, Ars Combin. 30 (1990), 161-176. (Annotated scanned copy)
%H Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/trans/">Transitive Graphs</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Vertex-TransitiveGraph.html">Vertex-Transitive Graph</a>
%e Triangle begins, n >= 1, 0 <= k < n:
%e 1;
%e 1, 1;
%e 1, 0, 1;
%e 1, 1, 1, 1;
%e 1, 0, 1, 0, 1;
%e 1, 1, 2, 2, 1, 1;
%e 1, 0, 1, 0, 1, 0, 1;
%e 1, 1, 2, 3, 3, 2, 1, 1;
%e 1, 0, 2, 0, 3, 0, 2, 0, 1;
%e 1, 1, 2, 3, 4, 4, 3, 2, 1, 1;
%e 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1;
%e 1, 1, 4, 7, 11, 13, 13, 11, 7, 4, 1, 1;
%e 1, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1;
%e 1, 1, 2, 3, 6, 6, 9, 9, 6, 6, 3, 2, 1, 1;
%e 1, 0, 3, 0, 8, 0, 12, 0, 12, 0, 8, 0, 3, 0, 1;
%e 1, 1, 3, 7, 16, 27, 40, 48, 48, 40, 27, 16, 7, 3, 1, 1;
%e 1, 0, 1, 0, 4, 0, 7, 0, 10, 0, 7, 0, 4, 0, 1, 0, 1;
%e 1, 1, 4, 7, 16, 24, 38, 45, 54, 54, 45, 38, 24, 16, 7, 4, 1, 1;
%e ...
%Y Columns k=2..12 (even n only for odd k) are A023645, A023646, A023647, A023640, A023641, A023642, A023643, A023644, A023637, A023638, A023639.
%Y Row sums are A006799.
%Y Cf. A319368, A319372.
%K nonn,tabl
%O 1,18
%A _Andrew Howroyd_, Sep 17 2018
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