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A363044 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.

%I A363044 #4 May 14 2023 11:41:47
%S A363044 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 A363044 1,109,1475,5077,4097,357,1,0,1,247,6623,55005,129904,67529,1770,1,0,
%U A363044 1,564,28540,505098,3378636,5792187,1999810,11734,1
%N A363044 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 A363044 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 A363044 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 A363044 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 A363044 T(n,1) = 0 for n >= 2. (The only connected graph with packing chromatic number 1 is the 1-node graph.)
%F A363044 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 A363044 T(n,n) = 1. (The only connected graph with n nodes and packing chromatic number n is the complete graph on n nodes.)
%e A363044 Triangle begins:
%e A363044   n\k| 1  2   3     4      5       6       7       8     9 10
%e A363044   ---+-------------------------------------------------------
%e A363044    1 | 1
%e A363044    2 | 0  1
%e A363044    3 | 0  1   1
%e A363044    4 | 0  1   4     1
%e A363044    5 | 0  1   9    10      1
%e A363044    6 | 0  1  21    61     28       1
%e A363044    7 | 0  1  48   305    409      89       1
%e A363044    8 | 0  1 109  1475   5077    4097     357       1
%e A363044    9 | 0  1 247  6623  55005  129904   67529    1770     1
%e A363044   10 | 0  1 564 28540 505098 3378636 5792187 1999810 11734  1
%Y A363044 Cf. A001349 (row sums), A084269 (chromatic number), A363043 (not necessarily connected).
%K A363044 nonn,tabl
%O A363044 1,9
%A A363044 _Pontus von Brömssen_, May 14 2023