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A282996 T(n,k) is the number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.

%I A282996 #9 Oct 20 2023 15:01:06
%S A282996 2,4,4,7,11,7,13,33,33,13,24,98,163,98,24,44,291,803,803,291,44,81,
%T A282996 865,3971,6547,3971,865,81,149,2570,19587,53389,53389,19587,2570,149,
%U A282996 274,7637,96693,435027,720417,435027,96693,7637,274,504,22693,477297,3546870
%N A282996 T(n,k) is the number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.
%H A282996 R. H. Hardin, <a href="/A282996/b282996.txt">Table of n, a(n) for n = 1..312</a>
%F A282996 Empirical for column k:
%F A282996 k=1: a(n) = a(n-1) +a(n-2) +a(n-3);
%F A282996 k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4);
%F A282996 k=3: [order 9];
%F A282996 k=4: [order 15];
%F A282996 k=5: [order 36];
%F A282996 k=6: [order 69].
%e A282996 Table starts:
%e A282996 ...2.....4........7.........13...........24.............44...............81
%e A282996 ...4....11.......33.........98..........291............865.............2570
%e A282996 ...7....33......163........803.........3971..........19587............96693
%e A282996 ..13....98......803.......6547........53389.........435027..........3546870
%e A282996 ..24...291.....3971......53389.......720417........9706901........130854309
%e A282996 ..44...865....19587.....435027......9706901......216173426.......4817792042
%e A282996 ..81..2570....96693....3546870....130854309.....4817792042.....177509416175
%e A282996 .149..7637...477297...28911809...1763845523...107354061547....6539125324144
%e A282996 .274.22693..2355925..235681253..23775564134..2392171690343..240894164469261
%e A282996 .504.67432.11629027.1921212987.320481684651.53305366529469.8874303766960833
%e A282996 Some solutions for n=5 and k=4:
%e A282996 ..0..1..1..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
%e A282996 ..0..0..0..1. .0..0..0..1. .0..1..0..0. .1..0..0..0. .0..1..0..1
%e A282996 ..0..1..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..0..0
%e A282996 ..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..1..0. .0..0..0..0
%e A282996 ..0..0..0..1. .0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..1..0
%Y A282996 Columns are A000073(n+3), A282990, A282991, A282992, A282993, A282994, A282995.
%Y A282996 Diagonal is A067968.
%K A282996 nonn,tabl
%O A282996 1,1
%A A282996 _R. H. Hardin_, Feb 26 2017