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A291044 Irregular triangle read by rows: number of maximal irredundant sets of size k in the n-cycle graph. 2
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,tabf
AUTHOR
Andrew Howroyd, Aug 16 2017
STATUS
approved

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Last modified April 23 22:36 EDT 2024. Contains 371917 sequences. (Running on oeis4.)