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

1,4

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.

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.

Formula

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

Example

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.

Crossrefs

Row sums of A291055.

Sequence in context: A348536 A245963 A382138 * A346914 A033778 A091586

Adjacent sequences: A291372 A291373 A291374 * A291376 A291377 A291378

Keyword

nonn,tabf

Author

Andrew Howroyd, Aug 23 2017

Status

approved