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A291044 Irregular triangle read by rows: number of maximal irredundant sets of size k in the n-cycle graph.

%I A291044 #16 May 29 2025 10:40:13
%S A291044 0,2,0,3,0,0,6,0,0,10,0,0,9,2,0,0,0,14,0,0,0,8,6,0,0,0,3,27,0,0,0,0,
%T A291044 60,2,0,0,0,0,33,33,0,0,0,0,9,84,6,0,0,0,0,0,91,52,0,0,0,0,0,14,196,2,
%U A291044 0,0,0,0,0,3,280,60,0,0,0,0,0,0,200,272,6
%N A291044 Irregular triangle read by rows: number of maximal irredundant sets of size k in the n-cycle graph.
%C A291044 For each row, k lies in the range 0..floor(n/2). The upper end of the range is the upper irredundance number of the graph.
%H A291044 Andrew Howroyd, <a href="/A291044/b291044.txt">Table of n, a(n) for n = 2..991</a>
%H A291044 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CycleGraph.html">Cycle Graph</a>.
%H A291044 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>.
%F A291044 T(n,k) = 0 for k < ceiling(n/3).
%F A291044 Sum_{k=0..floor(n/2)} T(n,k) = A286954(n). - _Eric W. Weisstein_, Jun 11 2021
%e A291044 Triangle begins:
%e A291044   0, 2;
%e A291044   0, 3;
%e A291044   0, 0, 6;
%e A291044   0, 0, 10;
%e A291044   0, 0,  9   2;
%e A291044   0, 0,  0, 14;
%e A291044   0, 0,  0,  8,  6;
%e A291044   0, 0,  0,  3, 27;
%e A291044   0, 0,  0,  0, 60,  2;
%e A291044   0, 0,  0,  0, 33, 33;
%e A291044   0, 0,  0,  0,  9, 84,   6;
%e A291044   0, 0,  0,  0,  0, 91,  52;
%e A291044   0, 0,  0,  0,  0, 14, 196, 2;
%e A291044   ...
%e A291044 As polynomials these are 2*x; 3*x; 6*x^2; 10*x^2; 9*x^2 + 2*x^3; etc.
%Y A291044 Row sums are A286954.
%K A291044 nonn,tabf
%O A291044 2,2
%A A291044 _Andrew Howroyd_, Aug 16 2017