A369227 Triangle read by rows: T(n,k) is the number of uniquely colorable simple graphs on n nodes with chromatic number k = 1..n.

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 3, 1, 1, 1, 17, 12, 3, 1, 1, 1, 44, 72, 12, 3, 1, 1, 1, 182, 856, 127, 12, 3, 1, 1, 1, 730, 17018, 3426, 127, 12, 3, 1, 1, 1, 4032, 531568, 221188, 4938, 127, 12, 3, 1, 1, 1, 25598

Offset

1,8

Links

Table of n, a(n) for n=1..57.

Eric Weisstein's World of Mathematics, Chromatic Number.

Eric Weisstein's World of Mathematics, Simple Graph.

Eric Weisstein's World of Mathematics, Uniquely Colorable Graph.

Formula

T(n,1) = 1.

T(n,2) = A005142(n).

T(n,3) = A348222(n).

T(n,n) = 1.

Sum_{k=1..n} T(n,k) = A369223(n).

Example

Triangle read by rows:
  1
  1,     1
  1,     1,      1
  1,     3,      1,      1
  1,     5,      3,      1,    1
  1,    17,     12,      3,    1,   1
  1,    44,     72,     12,    3,   1,  1
  1,   182,    856,    127,   12,   3,  1, 1
  1,   730,  17018,   3426,  127,  12,  3, 1, 1
  1,  4032, 531568, 221188, 4938, 127, 12, 3, 1, 1
  1, 25598,    ...

Crossrefs

Cf. A005142, A348222, A369223.

Sequence in context: A255811 A131268 A109221 * A360908 A351347 A046643

Adjacent sequences: A369224 A369225 A369226 * A369228 A369229 A369230

Keyword

nonn,tabl,more

Author

Eric W. Weisstein, Jan 16 2024

Status

approved