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).

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, 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, 1, 4, 10, 12, 13, 11, 7, 4, 1, 1, 0, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1

Offset: 1

Author

Andrew Howroyd, Sep 17 2018

Keywords

• nonn
• tabl

Examples

			Triangle begins:
  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,  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, 1, 4, 10, 12, 13, 11,  7,  4,  1,  1;
  0, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
  0, 0, 1, 3,  5,  6,  8,  9,  6,  6,  3,  2,  1,  1;
  0, 0, 1, 0,  7,  0, 12,  0, 12,  0,  8,  0,  3,  0, 1;
  0, 0, 1, 4, 13, 25, 39, 47, 48, 40, 27, 16,  7,  3, 1, 1;
  0, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
  0, 0, 1, 5, 12, 23, 36, 45, 53, 54, 45, 38, 24, 16, 7, 4, 1, 1;
  ...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..496
• B. D. McKay and G. F. Royle, The transitive graphs with at most 26 vertices, Ars Combin. 30 (1990), 161-176. (Annotated scanned copy)
• Gordon Royle, Transitive Graphs
• Eric Weisstein's World of Mathematics, Vertex-Transitive Graph.

Crossrefs

Row sums are A006800.

Cf. A319367.

Formula

T(n,k) = Sum_{d|n} moebius(n/d) * A319367(d,k).