A380197 Number of ways to choose a simple labeled graph on [n] and properly color the vertices using the minimum number of colors.

1, 1, 3, 25, 423, 16261, 1266843, 200830225, 65750156223, 42834021462061, 55174125327583923

Offset

0,3

Comments

a(n) is the chromatic polynomial evaluated at the chromatic number of a graph summed over all simple labeled graphs on [n].

Links

Table of n, a(n) for n=0..10.

Eric Weisstein's World of Mathematics, Chromatic Number.

Eric Weisstein's World of Mathematics, Chromatic Polynomial.

Mathematica

(* this code only returns a(0) - a(7) using precomputed data in Mathematica 12 *)
nog = {1, 2, 4, 11, 34, 156, 1044}; Prepend[Table[Total[n!/Table[GraphData[{n, i}, AutomorphismCount"], {i, 1, nog[[n]]}]*Table[GraphData[{n, i}, ChromaticPolynomial"][GraphData[{n, i}, "ChromaticNumber"]], {i, 1, nog[[n]]}]], {n, 1, 7}], 1]

Crossrefs

Cf. A006125, A372920, A229048, A084268.

Sequence in context: A245309 A074708 A323217 * A160143 A009843 A366007

Adjacent sequences: A380194 A380195 A380196 * A380198 A380199 A380200

Keyword

nonn,more

Author

Geoffrey Critzer, Jan 22 2025

Extensions

a(8)-a(10) from Andrew Howroyd, Jan 22 2025

Status

approved