A298660 - OEIS

%I #4 Jan 24 2018 10:11:44

%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,19,19,23,5,8,49,23,40,23,49,8,

%T 13,95,34,85,85,34,95,13,21,177,63,173,177,173,63,177,21,34,359,96,

%U 322,431,431,322,96,359,34,55,705,147,635,876,1116,876,635,147,705,55,89,1351

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0...1...1....2....3.....5.....8.....13......21......34.......55........89

%C ..1...3...7...13...23....49....95....177.....359.....705.....1351......2689

%C ..1...7..15...19...23....34....63.....96.....147.....233......368.......588

%C ..2..13..19...40...85...173...322....635....1325....2806.....5877.....12293

%C ..3..23..23...85..177...431...876...2137....5002...11687....27591.....64253

%C ..5..49..34..173..431..1116..2562...6711...17405...48462...125671....334571

%C ..8..95..63..322..876..2562..7964..24801...74358..242072...745571...2349275

%C .13.177..96..635.2137..6711.24801..89543..322065.1213296..4468276..16453935

%C .21.359.147.1325.5002.17405.74358.322065.1367704.6098314.26543249.116098205

%H R. H. Hardin, <a href="/A298660/b298660.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-3) -10*a(n-4) +4*a(n-5) for n>6

%F k=3: [order 18] for n>19

%F k=4: [order 72] for n>73

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A297852.

%Y Column 3 is A298050.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 24 2018