A300138 - OEIS

%I #4 Feb 26 2018 08:03:18

%S 1,1,1,1,1,1,1,1,1,1,1,2,16,2,1,1,5,17,17,5,1,1,9,88,27,88,9,1,1,22,

%T 209,204,204,209,22,1,1,45,673,667,2156,667,673,45,1,1,101,1898,3273,

%U 11439,11439,3273,1898,101,1,1,218,5663,13765,80126,98708,80126,13765,5663,218

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .1...1....1.....1.......1.........1..........1............1..............1

%C .1...1....1.....2.......5.........9.........22...........45............101

%C .1...1...16....17......88.......209........673.........1898...........5663

%C .1...2...17....27.....204.......667.......3273........13765..........61625

%C .1...5...88...204....2156.....11439......80126.......539828........3690822

%C .1...9..209...667...11439.....98708....1118800.....12484789......140924631

%C .1..22..673..3273...80126...1118800...20405641....375468115.....6965745267

%C .1..45.1898.13765..539828..12484789..375468115..11565870189...357938887736

%C .1.101.5663.61625.3690822.140924631.6965745267.357938887736.18502726008627

%H R. H. Hardin, <a href="/A300138/b300138.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>5

%F k=3: [order 10] for n>12

%F k=4: [order 28] for n>29

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A052962(n-2).

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Feb 26 2018