A317153 - OEIS

%I #4 Jul 22 2018 15:48:28

%S 1,2,2,4,4,4,8,14,14,8,16,28,36,28,16,32,94,102,102,94,32,64,284,389,

%T 416,389,284,64,128,752,1251,2313,2313,1251,752,128,256,2244,4091,

%U 10682,19580,10682,4091,2244,256,512,6532,13931,49746,120427,120427,49746

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5, 7 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....36.....102......389......1251........4091........13931

%C ...8...28...102.....416.....2313.....10682.......49746.......244887

%C ..16...94...389....2313....19580....120427......786868......5565982

%C ..32..284..1251...10682...120427....960577.....8398085.....79355311

%C ..64..752..4091...49746...786868...8398085...100639070...1322153771

%C .128.2244.13931..244887..5565982..79355311..1322153771..24402104731

%C .256.6532.46536.1177228.37386216.704559110.16079639203.409040712216

%H R. H. Hardin, <a href="/A317153/b317153.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>16

%F k=4: [order 69] for n>70

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304341.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 22 2018