A368987 Triangle read by rows: T(n,k) is the number of unlabeled point-determining graphs with n nodes and k edges, n >= 0, 0 <= k <= n*(n - 1)/2.

1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 3, 3, 4, 2, 1, 0, 1, 0, 0, 0, 1, 3, 6, 11, 14, 13, 12, 9, 5, 2, 1, 0, 1, 0, 0, 0, 1, 1, 5, 15, 31, 50, 77, 89, 94, 83, 61, 37, 24, 11, 5, 2, 1, 0, 1, 0, 0, 0, 0, 1, 3, 11, 35, 89, 197, 371, 603, 861, 1068, 1154, 1098, 926, 679, 445, 257, 134, 65, 30, 11, 5, 2, 1, 0, 1

Offset

0,12

Comments

Point-determining graphs are also called mating graphs.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..175 (rows 0..10)

Ira M. Gessel and Ji Li, Enumeration of point-determining graphs, J. Combinatorial Theory Ser. A 118 (2011), 591-612.

Example

Triangle begins:
[0] 1;
[1] 1;
[2] 0, 1;
[3] 0, 1, 0, 1;
[4] 0, 0, 1, 2, 1, 0,  1;
[5] 0, 0, 1, 1, 3, 3,  4,  2,  1,  0,  1;
[6] 0, 0, 0, 1, 3, 6, 11, 14, 13, 12,  9,  5,  2,  1,  0,  1;
[7] 0, 0, 0, 1, 1, 5, 15, 31, 50, 77, 89, 94, 83, 61, 37, 24, 11, 5, 2, 1, 0, 1;

Crossrefs

Row sums are A004110.

Cf. A123551 (same row sums), A369283 (labeled).

Sequence in context: A015738 A333815 A308103 * A115604 A128617 A116488

Adjacent sequences: A368984 A368985 A368986 * A368988 A368989 A368990

Keyword

nonn,tabf

Author

Andrew Howroyd, Jan 15 2024

Status

approved