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

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, 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, 0, 0, 0, 0, 0, 3, 280, 60, 0, 0, 0, 0, 0, 0, 200, 272, 6

Offset: 2

Author

Andrew Howroyd, Aug 16 2017

Keywords

• nonn
• tabf

Comments

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.

Examples

			Triangle begins:
  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, 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;
  ...
As polynomials these are 2*x; 3*x; 6*x^2; 10*x^2; 9*x^2 + 2*x^3; etc.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..991
• Eric Weisstein's World of Mathematics, Cycle Graph.
• Eric Weisstein's World of Mathematics, Maximal Irredundant Set.

Crossrefs

Row sums are A286954.

Formula

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

Sum_{k=0..floor(n/2)} T(n,k) = A286954(n). - Eric W. Weisstein, Jun 11 2021