A319372 Triangle read by rows: T(n,k) is the number of Cayley 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, 2, 4, 4, 2, 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

Comments

First differs from A319367 in row 10.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..496

Gordon Royle, Transitive Graphs

Eric Weisstein's World of Mathematics, Cayley Graph

Wikipedia, Cayley 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, 2,  4,  4,  2,  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,  7,  0, 11,  0, 11,  0,  7,  0,  3,  0, 1;
  1, 1, 3, 7, 15, 26, 39, 47, 47, 39, 26, 15,  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, 23, 38, 45, 53, 53, 45, 38, 23, 16, 7, 4, 1, 1;
  ...

Crossrefs

Column k=3 is aerated A319374.

Row sums are A185959.

Cf. A319367, A319368.

Sequence in context: A263087 A204433 A004578 * A319367 A234514 A343453

Adjacent sequences: A319369 A319370 A319371 * A319373 A319374 A319375

Keyword

nonn,tabl

Author

Andrew Howroyd, Sep 17 2018

Status

approved