A282996 - OEIS

%I #9 Oct 20 2023 15:01:06

%S 2,4,4,7,11,7,13,33,33,13,24,98,163,98,24,44,291,803,803,291,44,81,

%T 865,3971,6547,3971,865,81,149,2570,19587,53389,53389,19587,2570,149,

%U 274,7637,96693,435027,720417,435027,96693,7637,274,504,22693,477297,3546870

%N 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 R. H. Hardin, <a href="/A282996/b282996.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2) +a(n-3);

%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4);

%F k=3: [order 9];

%F k=4: [order 15];

%F k=5: [order 36];

%F k=6: [order 69].

%e Table starts:

%e ...2.....4........7.........13...........24.............44...............81

%e ...4....11.......33.........98..........291............865.............2570

%e ...7....33......163........803.........3971..........19587............96693

%e ..13....98......803.......6547........53389.........435027..........3546870

%e ..24...291.....3971......53389.......720417........9706901........130854309

%e ..44...865....19587.....435027......9706901......216173426.......4817792042

%e ..81..2570....96693....3546870....130854309.....4817792042.....177509416175

%e .149..7637...477297...28911809...1763845523...107354061547....6539125324144

%e .274.22693..2355925..235681253..23775564134..2392171690343..240894164469261

%e .504.67432.11629027.1921212987.320481684651.53305366529469.8874303766960833

%e Some solutions for n=5 and k=4:

%e ..0..1..1..0. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0

%e ..0..0..0..1. .0..0..0..1. .0..1..0..0. .1..0..0..0. .0..1..0..1

%e ..0..1..1..0. .1..0..0..0. .0..1..0..1. .0..1..0..1. .0..0..0..0

%e ..0..0..0..0. .1..0..0..0. .0..0..1..0. .1..0..1..0. .0..0..0..0

%e ..0..0..0..1. .0..0..1..0. .1..0..0..1. .0..0..0..0. .0..0..1..0

%Y Columns are A000073(n+3), A282990, A282991, A282992, A282993, A282994, A282995.

%Y Diagonal is A067968.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 26 2017