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A319368 Triangle read by rows: T(n,k) is the number of simple connected vertex transitive graphs with n nodes and valency k, (0 <= k < n).

%I A319368 #11 Feb 01 2025 23:17:52
%S A319368 1,0,1,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,2,1,1,0,0,1,0,1,0,1,0,0,1,2,3,2,
%T A319368 1,1,0,0,1,0,3,0,2,0,1,0,0,1,3,3,4,3,2,1,1,0,0,1,0,2,0,2,0,1,0,1,0,0,
%U A319368 1,4,10,12,13,11,7,4,1,1,0,0,1,0,3,0,4,0,3,0,1,0,1
%N A319368 Triangle read by rows: T(n,k) is the number of simple connected vertex transitive graphs with n nodes and valency k, (0 <= k < n).
%H A319368 Andrew Howroyd, <a href="/A319368/b319368.txt">Table of n, a(n) for n = 1..496</a>
%H A319368 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 A319368 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/trans/">Transitive Graphs</a>
%H A319368 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-TransitiveGraph.html">Vertex-Transitive Graph</a>.
%F A319368 T(n,k) = Sum_{d|n} moebius(n/d) * A319367(d,k).
%e A319368 Triangle begins:
%e A319368   1;
%e A319368   0, 1;
%e A319368   0, 0, 1;
%e A319368   0, 0, 1, 1;
%e A319368   0, 0, 1, 0,  1;
%e A319368   0, 0, 1, 2,  1,  1;
%e A319368   0, 0, 1, 0,  1,  0,  1;
%e A319368   0, 0, 1, 2,  3,  2,  1,  1;
%e A319368   0, 0, 1, 0,  3,  0,  2,  0,  1;
%e A319368   0, 0, 1, 3,  3,  4,  3,  2,  1,  1;
%e A319368   0, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
%e A319368   0, 0, 1, 4, 10, 12, 13, 11,  7,  4,  1,  1;
%e A319368   0, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
%e A319368   0, 0, 1, 3,  5,  6,  8,  9,  6,  6,  3,  2,  1,  1;
%e A319368   0, 0, 1, 0,  7,  0, 12,  0, 12,  0,  8,  0,  3,  0, 1;
%e A319368   0, 0, 1, 4, 13, 25, 39, 47, 48, 40, 27, 16,  7,  3, 1, 1;
%e A319368   0, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
%e A319368   0, 0, 1, 5, 12, 23, 36, 45, 53, 54, 45, 38, 24, 16, 7, 4, 1, 1;
%e A319368   ...
%Y A319368 Row sums are A006800.
%Y A319368 Cf. A319367.
%K A319368 nonn,tabl
%O A319368 1,19
%A A319368 _Andrew Howroyd_, Sep 17 2018