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Triangle read by rows: T(n,k) is the number of unlabeled simple graphs with n vertices and Grundy number k, 0 <= k < n.
0

%I #18 Feb 03 2025 15:50:33

%S 1,1,1,1,2,1,1,5,4,1,1,8,18,6,1,1,15,67,63,9,1

%N Triangle read by rows: T(n,k) is the number of unlabeled simple graphs with n vertices and Grundy number k, 0 <= k < n.

%C The Grundy number of a graph is the largest k such that the graph has a greedy k-coloring for some ordering of its vertices. - _Charles R Greathouse IV_, Oct 16 2015

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000172">The Grundy number of a graph</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Grundy_number">Grundy number</a>.

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 5, 4, 1;

%e 1, 8, 18, 6, 1;

%e 1, 15, 67, 63, 9, 1;

%e ...

%Y Row sums are A000088.

%K nonn,tabl,more

%O 1,5

%A _Christian Stump_, Oct 14 2015