A355067 a(n) is the failed skew zero forcing number of P^3_n.

0, 1, 3, 3, 4, 4, 6, 5, 6, 7, 9, 8, 9, 10, 12, 11, 12, 13, 15, 14, 15, 16, 18, 17, 18, 19, 21, 20, 21, 22, 24, 23, 24, 25, 27, 26, 27, 28, 30, 29, 30, 31, 33, 32, 33, 34, 36, 35, 36, 37, 39, 38, 39, 40, 42, 41, 42, 43

Offset

3,3

Comments

P^3_n is the cube of path graph P_n.

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 skew color change rule will not result in all vertices being filled.

Links

Georg Fischer, Table of n, a(n) for n = 3..1000

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 (1,0,0,1,-1).

Formula

a(n) = 3*floor((n-1)/4) + cos((n*Pi)/2) for n > 7.

G.f.: x^3*(1 + 2*x + x^3 - x^4 - x^6 + x^8)/((1 - x)^2*(1 + x)*(1 + x^2)). - Stefano Spezia, Jul 15 2022

Crossrefs

Sequence in context: A369218 A097356 A083522 * A108942 A025561 A342169

Adjacent sequences: A355064 A355065 A355066 * A355068 A355069 A355070

Keyword

nonn,easy

Author

Aidan Johnson, Darren Narayan, and Andrew E. Vick, Jul 14 2022

Status

approved