A291375 - OEIS

%I #7 Aug 23 2017 23:36:22

%S 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 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 0,0,0,0,14,150,20,0,0,0,0,0,1,155,112,1

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

%C 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 Andrew Howroyd, <a href="/A291375/b291375.txt">Table of n, a(n) for n = 1..990</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MaximalIrredundantSet.html">Maximal Irredundant Set</a>

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

%F T(n,k) = 0 for k < ceiling(n/3).

%e Triangle begins:

%e 0, 1;

%e 0, 2;

%e 0, 1, 1;

%e 0, 0, 4;

%e 0, 0, 5,  1;

%e 0, 0, 2,  6;

%e 0, 0, 0, 12,  1;

%e 0, 0, 0,  8,  9;

%e 0, 0, 0,  1, 25,  1;

%e 0, 0, 0,  0, 28, 12;

%e 0, 0, 0,  0, 12, 44,  1;

%e 0, 0, 0,  0,  2, 68, 16;

%e ...

%e As polynomials these are: x; 2*x; x + x^2; 4*x^2; 5*x^2 + x^3; etc.

%Y Row sums of A291055.

%K nonn,tabf

%O 1,4

%A _Andrew Howroyd_, Aug 23 2017