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).
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, 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, 4, 7, 11, 13, 13, 11, 7, 4, 1, 1, 1, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1
Offset: 1
Examples
Triangle begins, n >= 1, 0 <= k < n: 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, 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, 4, 7, 11, 13, 13, 11, 7, 4, 1, 1; 1, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1; 1, 1, 2, 3, 6, 6, 9, 9, 6, 6, 3, 2, 1, 1; 1, 0, 3, 0, 8, 0, 12, 0, 12, 0, 8, 0, 3, 0, 1; 1, 1, 3, 7, 16, 27, 40, 48, 48, 40, 27, 16, 7, 3, 1, 1; 1, 0, 1, 0, 4, 0, 7, 0, 10, 0, 7, 0, 4, 0, 1, 0, 1; 1, 1, 4, 7, 16, 24, 38, 45, 54, 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.