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

2,2

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.

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, Irredundant Set

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

Example

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.

Crossrefs

Row sums are A286954.

Sequence in context: A113303 A080089 A322841 * A113290 A078442 A175663

Adjacent sequences: A291041 A291042 A291043 * A291045 A291046 A291047

Keyword

nonn,tabf

Author

Andrew Howroyd, Aug 16 2017

Status

approved