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A291375 Irregular triangle read by rows: number of maximal irredundant sets of size k in the n-path graph.

%I A291375 #11 May 29 2025 10:40:30
%S A291375 0,1,0,2,0,1,1,0,0,4,0,0,5,1,0,0,2,6,0,0,0,12,1,0,0,0,8,9,0,0,0,1,25,
%T A291375 1,0,0,0,0,28,12,0,0,0,0,12,44,1,0,0,0,0,2,68,16,0,0,0,0,0,48,73,1,0,
%U A291375 0,0,0,0,14,150,20,0,0,0,0,0,1,155,112,1
%N A291375 Irregular triangle read by rows: number of  maximal irredundant sets of size k in the n-path graph.
%C A291375 For each row, k lies in the range 0..ceiling(n/2). The upper end of the range is the upper irredundance number of the graph.
%H A291375 Andrew Howroyd, <a href="/A291375/b291375.txt">Table of n, a(n) for n = 1..990</a>
%H A291375 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>.
%H A291375 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PathGraph.html">Path Graph</a>.
%F A291375 T(n,k) = 0 for k < ceiling(n/3).
%e A291375 Triangle begins:
%e A291375   0, 1;
%e A291375   0, 2;
%e A291375   0, 1, 1;
%e A291375   0, 0, 4;
%e A291375   0, 0, 5,  1;
%e A291375   0, 0, 2,  6;
%e A291375   0, 0, 0, 12,  1;
%e A291375   0, 0, 0,  8,  9;
%e A291375   0, 0, 0,  1, 25,  1;
%e A291375   0, 0, 0,  0, 28, 12;
%e A291375   0, 0, 0,  0, 12, 44,  1;
%e A291375   0, 0, 0,  0,  2, 68, 16;
%e A291375   ...
%e A291375 As polynomials these are: x; 2*x; x + x^2; 4*x^2; 5*x^2 + x^3; etc.
%Y A291375 Row sums of A291055.
%K A291375 nonn,tabf
%O A291375 1,4
%A A291375 _Andrew Howroyd_, Aug 23 2017