cp's OEIS Frontend

A197054 T(n,k)=Number of nXk 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.

%I A197054 #19 Feb 16 2025 08:33:15
%S A197054 1,2,2,2,2,2,3,4,4,3,4,6,10,6,4,5,10,18,18,10,5,7,16,38,42,38,16,7,9,
%T A197054 26,78,108,108,78,26,9,12,42,156,274,358,274,156,42,12,16,68,320,692,
%U A197054 1132,1132,692,320,68,16,21,110,654,1754,3580,4468,3580,1754,654,110,21,28
%N A197054 T(n,k)=Number of nXk 0..4 arrays with each element equal to the number of its horizontal and vertical zero neighbors.
%C A197054 Every 0 is next to 0 0's, every 1 is next to 1 0's, every 2 is next to 2 0's, every 3 is next to 3 0's, every 4 is next to 4 0's
%C A197054 Also, the number of maximal independent vertex sets in the grid graph P_n X P_k. - _Andrew Howroyd_, May 16 2017
%H A197054 R. H. Hardin, <a href="/A197054/b197054.txt">Table of n, a(n) for n = 1..364</a>
%H A197054 Oh, Seungsang. "Maximal independent sets on a grid graph." Discrete Mathematics 340.12 (2017): 2762-2768. Also <a href="http://arxiv.org/abs/1709.03678">arXiv:1709.03678</a>.
%H A197054 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>
%H A197054 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalIndependentVertexSet.html">Maximal Independent Vertex Set</a>
%e A197054 Table starts
%e A197054 ..1...2....2.....3......4.......5........7.........9.........12..........16
%e A197054 ..2...2....4.....6.....10......16.......26........42.........68.........110
%e A197054 ..2...4...10....18.....38......78......156.......320........654........1326
%e A197054 ..3...6...18....42....108.....274......692......1754.......4442.......11248
%e A197054 ..4..10...38...108....358....1132.....3580.....11382......36270......114992
%e A197054 ..5..16...78...274...1132....4468....17742.....70616.....281202.....1117442
%e A197054 ..7..26..156...692...3580...17742....88056....439338....2192602....10912392
%e A197054 ..9..42..320..1754..11382...70616...439338...2745186...17155374...106972582
%e A197054 .12..68..654..4442..36270..281202..2192602..17155374..134355866..1049189170
%e A197054 .16.110.1326.11248.114992.1117442.10912392.106972582.1049189170.10264692132
%e A197054 ...
%e A197054 Some solutions for n=6 k=4
%e A197054 ..0..2..1..0....0..2..0..1....2..0..2..0....0..3..0..2....0..2..1..0
%e A197054 ..2..0..1..2....1..1..1..1....0..2..1..1....2..0..4..0....3..0..1..2
%e A197054 ..1..1..2..0....1..0..2..0....2..1..0..2....1..2..0..2....0..3..1..0
%e A197054 ..0..3..0..3....1..1..1..1....0..2..2..0....0..1..1..1....2..0..1..2
%e A197054 ..3..0..4..0....0..3..0..2....3..0..1..2....1..1..1..0....1..1..2..0
%e A197054 ..0..3..0..2....2..0..3..0....0..2..1..0....1..0..1..1....0..2..0..2
%Y A197054 Column 1 is A000931(n+6).
%Y A197054 Column 2 is A006355(n+1).
%Y A197054 Columns 3-7 are A197049, A197050, A197051, A197052, A197053.
%Y A197054 Main diagonal is A197048.
%Y A197054 Cf. A089934 (independent sets), A218354 (dominating sets).
%K A197054 nonn,tabl
%O A197054 1,2
%A A197054 _R. H. Hardin_, Oct 09 2011