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Triangle read by rows: T(n,k) is the number of simple graphs with n unlabeled vertices and burning number k.
2

%I #17 Mar 11 2024 18:06:31

%S 1,0,2,0,3,1,0,8,2,1,0,23,9,1,1,0,94,56,4,1,1,0,534,494,11,3,1,1,0,

%T 4887,7401,43,10,3,1,1,0,76801,197605,213,35,9,3,1,1,0,2196200,

%U 9807208,1547,165,34,9,3,1,1

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

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000258">The burning number of a graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BurningNumber.html">Burning Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>.

%e Triangle begins:

%e 1;

%e 0, 2;

%e 0, 3, 1;

%e 0, 8, 2, 1;

%e 0, 23, 9, 1, 1;

%e 0, 94, 56, 4, 1, 1;

%e 0, 534, 494, 11, 3, 1, 1;

%e 0, 4887, 7401, 43, 10, 3, 1, 1;

%e 0, 76801, 197605, 213, 35, 9, 3, 1, 1;

%e 0, 2196200, 9807208, 1547, 165, 34, 9, 3, 1, 1;

%e ...

%Y Rows sums are A000088.

%Y Cf. A369278 (counts for connected graphs), A369279 (cooling number).

%K nonn,tabl,more

%O 1,3

%A _Christian Stump_, Oct 14 2015

%E Merged with near duplicate by _Andrew Howroyd_, Mar 11 2024