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A319367
Triangle read by rows: T(n,k) is the number of vertex transitive graphs with n nodes and valency k, (0 <= k < n).
9
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
1,18
LINKS
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
EXAMPLE
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;
...
CROSSREFS
Columns k=2..12 (even n only for odd k) are A023645, A023646, A023647, A023640, A023641, A023642, A023643, A023644, A023637, A023638, A023639.
Row sums are A006799.
Sequence in context: A204433 A004578 A319372 * A234514 A343453 A051031
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Sep 17 2018
STATUS
approved