A298834 - OEIS

%I #4 Jan 27 2018 07:35:27

%S 0,1,1,0,4,0,1,4,4,1,0,16,1,16,0,1,48,6,6,48,1,0,88,10,68,10,88,0,1,

%T 240,15,141,141,15,240,1,0,704,60,489,1590,489,60,704,0,1,1600,128,

%U 2774,3282,3282,2774,128,1600,1,0,4032,267,9849,27915,16551,27915,9849,267,4032,0

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

%C Table starts

%C .0....1...0.....1.......0........1.........0...........1.............0

%C .1....4...4....16......48.......88.......240.........704..........1600

%C .0....4...1.....6......10.......15........60.........128...........267

%C .1...16...6....68.....141......489......2774........9849.........39101

%C .0...48..10...141....1590.....3282.....27915......246700.......1055145

%C .1...88..15...489....3282....16551....226883.....1917869......16022685

%C .0..240..60..2774...27915...226883...5097700....70784399.....995832826

%C .1..704.128..9849..246700..1917869..70784399..2031564141...35098724239

%C .0.1600.267.39101.1055145.16022685.995832826.35098724239.1185589525594

%H R. H. Hardin, <a href="/A298834/b298834.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5)

%F k=3: [order 19] for n>20

%F k=4: [order 63] for n>65

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A298448.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 27 2018