A303690 - OEIS

%I #4 Apr 28 2018 09:34:35

%S 0,0,0,0,3,0,0,5,5,0,0,18,2,18,0,0,61,20,20,61,0,0,209,27,138,27,209,

%T 0,0,702,108,343,343,108,702,0,0,2381,191,1744,349,1744,191,2381,0,0,

%U 8069,599,5563,2809,2809,5563,599,8069,0,0,27330,1261,23963,4619,19068,4619

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C .0....3....5....18....61....209.....702.....2381.....8069.....27330......92581

%C .0....5....2....20....27....108.....191......599.....1261......3503.......8019

%C .0...18...20...138...343...1744....5563....23963....85439....343499....1279385

%C .0...61...27...343...349...2809....4619....29475....59695....312565.....749915

%C .0..209..108..1744..2809..19068...55382...273621...934066...4202604...15472710

%C .0..702..191..5563..4619..55382...99205...713542..1964803..10454428...36456925

%C .0.2381..599.23963.29475.273621..713542..5047477.16751184.100553061..399751263

%C .0.8069.1261.85439.59695.934066.1964803.16751184.58634971.399564046.1713589379

%H R. H. Hardin, <a href="/A303690/b303690.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

%F k=3: [order 16] for n>18

%F k=4: [order 31] for n>35

%F k=5: [order 93] for n>97

%e Some solutions for n=5 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 28 2018