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A319367 Triangle read by rows: T(n,k) is the number of simple vertex transitive graphs with n nodes and valency k, (0 <= k < n).

%I A319367 #14 Feb 01 2025 23:17:48
%S A319367 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 A319367 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 A319367 4,7,11,13,13,11,7,4,1,1,1,0,1,0,3,0,4,0,3,0,1,0,1
%N A319367 Triangle read by rows: T(n,k) is the number of simple vertex transitive graphs with n nodes and valency k, (0 <= k < n).
%H A319367 Andrew Howroyd, <a href="/A319367/b319367.txt">Table of n, a(n) for n = 1..496</a>
%H A319367 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 A319367 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/trans/">Transitive Graphs</a>.
%H A319367 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-TransitiveGraph.html">Vertex-Transitive Graph</a>.
%e A319367 Triangle begins, n >= 1, 0 <= k < n:
%e A319367   1;
%e A319367   1, 1;
%e A319367   1, 0, 1;
%e A319367   1, 1, 1, 1;
%e A319367   1, 0, 1, 0,  1;
%e A319367   1, 1, 2, 2,  1,  1;
%e A319367   1, 0, 1, 0,  1,  0,  1;
%e A319367   1, 1, 2, 3,  3,  2,  1,  1;
%e A319367   1, 0, 2, 0,  3,  0,  2,  0,  1;
%e A319367   1, 1, 2, 3,  4,  4,  3,  2,  1,  1;
%e A319367   1, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
%e A319367   1, 1, 4, 7, 11, 13, 13, 11,  7,  4,  1,  1;
%e A319367   1, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
%e A319367   1, 1, 2, 3,  6,  6,  9,  9,  6,  6,  3,  2,  1,  1;
%e A319367   1, 0, 3, 0,  8,  0, 12,  0, 12,  0,  8,  0,  3,  0, 1;
%e A319367   1, 1, 3, 7, 16, 27, 40, 48, 48, 40, 27, 16,  7,  3, 1, 1;
%e A319367   1, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
%e A319367   1, 1, 4, 7, 16, 24, 38, 45, 54, 54, 45, 38, 24, 16, 7, 4, 1, 1;
%e A319367   ...
%Y A319367 Columns k=2..12 (even n only for odd k) are A023645, A023646, A023647, A023640, A023641, A023642, A023643, A023644, A023637, A023638, A023639.
%Y A319367 Row sums are A006799.
%Y A319367 Cf. A319368, A319372.
%K A319367 nonn,tabl
%O A319367 1,18
%A A319367 _Andrew Howroyd_, Sep 17 2018