A317036 - OEIS

%I #4 Jul 19 2018 19:33:30

%S 1,2,2,4,4,4,8,14,14,8,16,28,30,28,16,32,94,82,82,94,32,64,284,280,

%T 354,280,284,64,128,752,842,1718,1718,842,752,128,256,2244,2591,7523,

%U 11368,7523,2591,2244,256,512,6532,8141,33798,66728,66728,33798,8141,6532,512

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2.....4......8.......16........32..........64..........128

%C ...2....4....14.....28.......94.......284.........752.........2244

%C ...4...14....30.....82......280.......842........2591.........8141

%C ...8...28....82....354.....1718......7523.......33798.......153703

%C ..16...94...280...1718....11368.....66728......417156......2714271

%C ..32..284...842...7523....66728....559097.....4939166.....46085330

%C ..64..752..2591..33798...417156...4939166....64983838....900623946

%C .128.2244..8141.153703..2714271..46085330...900623946..19235095363

%C .256.6532.25387.700615.17610616.435634601.12923660734.426907974013

%H R. H. Hardin, <a href="/A317036/b317036.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 15] for n>17

%F k=4: [order 65] for n>67

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A304341.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 19 2018