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

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

Offset: 1

Author

Andrew Howroyd, Aug 23 2017

Keywords

• nonn
• tabf

Comments

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.

Examples

			Triangle begins:
  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,  1;
  0, 0, 0,  0, 28, 12;
  0, 0, 0,  0, 12, 44,  1;
  0, 0, 0,  0,  2, 68, 16;
  ...
As polynomials these are: x; 2*x; x + x^2; 4*x^2; 5*x^2 + x^3; etc.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..990
• Eric Weisstein's World of Mathematics, Maximal Irredundant Set.
• Eric Weisstein's World of Mathematics, Path Graph.

Crossrefs

Row sums of A291055.

Formula

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