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A319372 Triangle read by rows: T(n,k) is the number of Cayley graphs with n nodes and valency k, (0 <= k < n).

%I A319372 #9 Feb 16 2025 08:33:56
%S A319372 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 A319372 1,1,1,0,2,0,3,0,2,0,1,1,1,2,2,4,4,2,2,1,1,1,0,1,0,2,0,2,0,1,0,1,1,1,
%U A319372 4,7,11,13,13,11,7,4,1,1,1,0,1,0,3,0,4,0,3,0,1,0,1
%N A319372 Triangle read by rows: T(n,k) is the number of Cayley graphs with n nodes and valency k, (0 <= k < n).
%C A319372 First differs from A319367 in row 10.
%H A319372 Andrew Howroyd, <a href="/A319372/b319372.txt">Table of n, a(n) for n = 1..496</a>
%H A319372 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/trans/">Transitive Graphs</a>
%H A319372 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CayleyGraph.html">Cayley Graph</a>
%H A319372 Wikipedia, <a href="https://en.wikipedia.org/wiki/Cayley_graph">Cayley graph</a>
%e A319372 Triangle begins, n >= 1, 0 <= k < n:
%e A319372   1;
%e A319372   1, 1;
%e A319372   1, 0, 1;
%e A319372   1, 1, 1, 1;
%e A319372   1, 0, 1, 0,  1;
%e A319372   1, 1, 2, 2,  1,  1;
%e A319372   1, 0, 1, 0,  1,  0,  1;
%e A319372   1, 1, 2, 3,  3,  2,  1,  1;
%e A319372   1, 0, 2, 0,  3,  0,  2,  0,  1;
%e A319372   1, 1, 2, 2,  4,  4,  2,  2,  1,  1;
%e A319372   1, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
%e A319372   1, 1, 4, 7, 11, 13, 13, 11,  7,  4,  1,  1;
%e A319372   1, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
%e A319372   1, 1, 2, 3,  6,  6,  9,  9,  6,  6,  3,  2,  1,  1;
%e A319372   1, 0, 3, 0,  7,  0, 11,  0, 11,  0,  7,  0,  3,  0, 1;
%e A319372   1, 1, 3, 7, 15, 26, 39, 47, 47, 39, 26, 15,  7,  3, 1, 1;
%e A319372   1, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
%e A319372   1, 1, 4, 7, 16, 23, 38, 45, 53, 53, 45, 38, 23, 16, 7, 4, 1, 1;
%e A319372   ...
%Y A319372 Column k=3 is aerated A319374.
%Y A319372 Row sums are A185959.
%Y A319372 Cf. A319367, A319368.
%K A319372 nonn,tabl
%O A319372 1,18
%A A319372 _Andrew Howroyd_, Sep 17 2018