A355399 a(n) is the failed skew zero forcing number of C^2_n.

0, 1, 2, 4, 3, 4, 6, 5, 6, 8, 6, 8, 10, 8, 10, 12, 10, 12, 14, 12, 14, 16, 14, 16, 18, 16, 18, 20, 18, 20, 22, 20, 22, 24, 22, 24, 26, 24, 26, 28, 26, 28, 30, 28, 30, 32, 30, 32, 34, 32, 34, 36, 34, 36, 38, 36, 38, 40, 38, 40, 42, 40, 42, 44, 42, 44, 46, 44, 46

Offset

3,3

Comments

Given a graph G where each vertex is initially considered filled or unfilled, we apply the skew color change rule, which states that a vertex v becomes filled if and only if it is the unique empty neighbor of some other vertex in the graph. The failed skew zero forcing number of G, is the maximum cardinality of any subset S of vertices on which repeated application of the color change rule will not result in all vertices being filled. Note that C^2_n = Ci_n(1,2) is the square of C_n.

Links

Table of n, a(n) for n=3..71.

T. Ansill, B. Jacob, J. Penzellna, and D. Saavedra, Failed skew zero forcing on a graph, Linear Algebra and its Applications, vol. 509 (2016), 40-63.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

a(n) = 2*floor(n/3) + 2*(ceiling(n/(3*floor(n/3) + 1)) - floor(n/(3*floor(n/3) +1 )) - 1) for n >= 11.

a(n) = 2*A008611(n-3) for n >= 11.

Crossrefs

Cf. A008611, A343648.

Sequence in context: A369430 A360691 A302707 * A224714 A089169 A291563

Adjacent sequences: A355396 A355397 A355398 * A355400 A355401 A355402

Keyword

nonn,easy

Author

Darren Narayan, Andrew E. Vick, and Aidan Johnson, Jun 30 2022

Extensions

More terms from Stefano Spezia, Jun 30 2022

Status

approved