A278280 - OEIS

A278280

T(n,k) = Number of n X k 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

%I #6 Sep 05 2022 19:40:56

%S 0,0,0,0,2,0,0,4,5,0,0,13,25,16,0,0,36,122,136,49,0,0,109,661,1461,

%T 839,153,0,0,317,3723,15728,16842,5013,476,0,0,938,20736,172091,

%U 350649,196726,30370,1483,0,0,2754,115446,1870365,7466627,7974561,2293193

%N T(n,k) = Number of n X k 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

%C Table starts

%C .0.....0.......0..........0.............0................0..................0

%C .0.....2.......4.........13............36..............109................317

%C .0.....5......25........122...........661.............3723..............20736

%C .0....16.....136.......1461.........15728...........172091............1870365

%C .0....49.....839......16842........350649..........7466627..........157609938

%C .0...153....5013.....196726.......7974561........329985827........13538466880

%C .0...476...30370....2293193.....180592726......14526103064......1158266740087

%C .0..1483..183403...26748095....4093629985.....640011857446.....99182079495633

%C .0..4619.1108525..311952675...92770708201...28192246592564...8491049196878995

%C .0.14388.6699034.3638315600.2102508396678.1241921389868057.726961954823301592

%H R. H. Hardin, <a href="/A278280/b278280.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

%F k=3: a(n) = 6*a(n-1) +3*a(n-2) -17*a(n-3) +19*a(n-5) -16*a(n-6) +8*a(n-7) for n>9.

%F k=4: [order 17] for n>19.

%F k=5: [order 44] for n>46.

%F k=6: [order 98] for n>101.

%F Empirical for row n:

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

%F n=3: [order 16].

%F n=4: [order 40].

%e Some solutions for n=4, k=4

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 16 2016