A317215 - OEIS

%I #4 Jul 23 2018 19:41:45

%S 1,1,1,1,4,1,1,8,8,1,1,24,23,24,1,1,82,107,107,82,1,1,272,537,959,537,

%T 272,1,1,908,2800,8433,8433,2800,908,1,1,3076,14652,76951,127358,

%U 76951,14652,3076,1,1,10444,77128,705763,1987026,1987026,705763,77128,10444,1

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C .1.....4......8.......24.........82...........272.............908

%C .1.....8.....23......107........537..........2800...........14652

%C .1....24....107......959.......8433.........76951..........705763

%C .1....82....537.....8433.....127358.......1987026........31138620

%C .1...272...2800....76951....1987026......53479785......1441577878

%C .1...908..14652...705763...31138620....1441577878.....66735041323

%C .1..3076..77128..6501334..489866621...39018757534...3103003384185

%C .1.10444.406622.59966772.7714180199.1057115569193.144406060742969

%H R. H. Hardin, <a href="/A317215/b317215.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: [order 16] for n>17

%F k=4: [order 49] for n>51

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A303882.

%Y Column 3 is A305949.

%Y Column 4 is A305950.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 23 2018