This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A355399 #35 Mar 28 2025 11:28:34 %S A355399 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, %T A355399 20,18,20,22,20,22,24,22,24,26,24,26,28,26,28,30,28,30,32,30,32,34,32, %U A355399 34,36,34,36,38,36,38,40,38,40,42,40,42,44,42,44,46,44,46 %N A355399 a(n) is the failed skew zero forcing number of C^2_n. %C A355399 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. %H A355399 Thomas Ansill, Bonnie Jacob, Jaime Penzellna, and Daniel Saavedra, <a href="https://doi.org/10.1016/j.laa.2016.07.019">Failed skew zero forcing on a graph</a>, Linear Algebra and its Applications, vol. 509 (2016), 40-63. %H A355399 Aidan Johnson, Andrew Vick, Rigoberto Flórez, and Darren A. Narayan, <a href="https://doi.org/10.3390/appliedmath5020032">Failed Skew Zero Forcing Numbers of Path Powers and Circulant Graphs</a>, AppliedMath (2025) Vol. 5, No. 2, 32. %H A355399 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1). %F A355399 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. %F A355399 a(n) = 2*A008611(n-3) for n >= 11. %Y A355399 Cf. A008611, A343648. %K A355399 nonn,easy %O A355399 3,3 %A A355399 _Darren Narayan_, _Andrew E. Vick_, and _Aidan Johnson_, Jun 30 2022 %E A355399 More terms from _Stefano Spezia_, Jun 30 2022