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A202979 T(n,k)=Number of nXk 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

%I A202979 #7 Jul 22 2025 16:55:10
%S A202979 1,1,1,1,2,1,1,4,4,1,1,7,17,7,1,1,14,58,58,14,1,1,31,215,385,215,31,1,
%T A202979 1,69,866,2582,2582,866,69,1,1,155,3507,17740,31380,17740,3507,155,1,
%U A202979 1,354,14120,122468,379788,379788,122468,14120,354,1,1,814,56921,846908
%N A202979 T(n,k)=Number of nXk 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.
%C A202979 Table starts
%C A202979 .1...1.....1......1........1..........1............1..............1
%C A202979 .1...2.....4......7.......14.........31...........69............155
%C A202979 .1...4....17.....58......215........866.........3507..........14120
%C A202979 .1...7....58....385.....2582......17740.......122468.........846908
%C A202979 .1..14...215...2582....31380.....379788......4590696.......55723864
%C A202979 .1..31...866..17740...379788....8071997....170937904.....3635245483
%C A202979 .1..69..3507.122468..4590696..170937904...6330398606...235362503738
%C A202979 .1.155.14120.846908.55723864.3635245483.235362503738.15305115754880
%H A202979 R. H. Hardin, <a href="/A202979/b202979.txt">Table of n, a(n) for n = 1..337</a>
%e A202979 Some solutions for n=5 k=3
%e A202979 ..1..1..1....0..1..1....1..1..0....0..0..0....1..1..1....0..1..1....0..0..0
%e A202979 ..1..1..1....1..1..1....1..1..0....0..1..1....1..1..1....0..1..1....1..1..1
%e A202979 ..1..1..0....1..1..1....1..0..0....1..1..1....0..0..0....1..1..0....1..1..1
%e A202979 ..1..1..1....0..0..0....1..1..1....1..1..1....1..1..0....1..1..1....1..1..0
%e A202979 ..0..1..1....0..0..0....0..1..1....1..1..1....1..1..0....0..1..1....0..0..0
%K A202979 nonn,tabl
%O A202979 1,5
%A A202979 _R. H. Hardin_ Dec 26 2011