The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #4 May 14 2023 11:41:47
%S 1,0,1,0,1,1,0,1,4,1,0,1,9,10,1,0,1,21,61,28,1,0,1,48,305,409,89,1,0,
%T 1,109,1475,5077,4097,357,1,0,1,247,6623,55005,129904,67529,1770,1,0,
%U 1,564,28540,505098,3378636,5792187,1999810,11734,1
%N Triangle read by rows: T(n,k) is the number of unlabeled connected graphs with n nodes and packing chromatic number k, 1 <= k <= n.
%C The concept of the packing chromatic number was introduced by Goddard et al. (2008) under the name broadcast chromatic number. The term packing chromatic number was introduced by Brešar et al. (2007).
%H Boštjan Brešar, Sandi Klavžar, and Douglas F. Rall, <a href="https://doi.org/10.1016/j.dam.2007.06.008">On the packing chromatic number of Cartesian products, hexagonal lattice, and trees</a>, Discrete Applied Mathematics 155 (2007), 2303-2311.
%H Wayne Goddard, Sandra M. Hedetniemi, Stephen T. Hedetniemi, John M. Harris, and Douglas F. Rall, <a href="https://www.researchgate.net/publication/220620011">Broadcast chromatic numbers of graphs</a>, Ars Combinatoria 86 (2008), 33-49.
%F T(n,1) = 0 for n >= 2. (The only connected graph with packing chromatic number 1 is the 1-node graph.)
%F T(n,2) = 1 for n >= 2. (The only connected graphs with packing chromatic number 2 are the star graphs on at least 2 nodes.)
%F T(n,n) = 1. (The only connected graph with n nodes and packing chromatic number n is the complete graph on n nodes.)
%e Triangle begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10
%e ---+-------------------------------------------------------
%e 1 | 1
%e 2 | 0 1
%e 3 | 0 1 1
%e 4 | 0 1 4 1
%e 5 | 0 1 9 10 1
%e 6 | 0 1 21 61 28 1
%e 7 | 0 1 48 305 409 89 1
%e 8 | 0 1 109 1475 5077 4097 357 1
%e 9 | 0 1 247 6623 55005 129904 67529 1770 1
%e 10 | 0 1 564 28540 505098 3378636 5792187 1999810 11734 1
%Y Cf. A001349 (row sums), A084269 (chromatic number), A363043 (not necessarily connected).
%K nonn,tabl
%O 1,9
%A _Pontus von Brömssen_, May 14 2023