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%I #9 Apr 26 2021 21:32:17
%S 1,1,0,1,1,0,1,4,1,0,1,10,9,1,0,1,33,58,19,1,0,1,94,457,266,34,1,0,1,
%T 319,3977,5574,1184,61,1,0,1,1053,39547,142039,72944,5393,102,1,0,1,
%U 3683,414891,4170606,5919941,1180610,26668,170,1,0
%N Triangle read by rows, 1 <= k <= n: T(n,k) is the number of (unlabeled) connected graphs with n nodes and zero forcing number k.
%C The zero forcing number of a graph can be defined as follows. Start with a blue/white coloring of the nodes. At each step, all white nodes, which are currently the unique white neighbor of a blue node, are colored blue. The zero forcing number is the minimum number of blue nodes in an initial coloring that leads to all nodes being blue after a finite number of steps.
%H Shaun M. Fallat, Leslie Hogben, Jephian C.-H. Lin, and Bryan L. Shader, <a href="https://www.ams.org/journals/notices/202002/rnoti-p257.pdf">The inverse eigenvalue problem of a graph, zero forcing, and related parameters</a>, Notices of the American Mathematical Society 67 (2020), 257-261.
%F T(n,1) = 1. (The path graph is the only n-node graph with zero forcing number 1.)
%F T(n,n-1) = 1 for n >= 2. (The complete graph is the only connected n-node graph with zero forcing number n-1.)
%F T(n,n) = 0 for n >= 2.
%e Triangle begins:
%e n\k 1 2 3 4 5 6 7 8 9 10
%e ------------------------------------------------------------------
%e 1: 1
%e 2: 1 0
%e 3: 1 1 0
%e 4: 1 4 1 0
%e 5: 1 10 9 1 0
%e 6: 1 33 58 19 1 0
%e 7: 1 94 457 266 34 1 0
%e 8: 1 319 3977 5574 1184 61 1 0
%e 9: 1 1053 39547 142039 72944 5393 102 1 0
%e 10: 1 3683 414891 4170606 5919941 1180610 26668 170 1 0
%Y Row sums: A001349.
%Y Cf. A343649.
%K nonn,tabl
%O 1,8
%A _Pontus von Brömssen_, Apr 24 2021
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