login
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.
7

%I #4 Jun 18 2018 07:40:12

%S 1,2,2,4,8,4,8,21,21,8,16,49,45,49,16,32,120,142,142,120,32,64,293,

%T 439,458,439,293,64,128,719,1261,1962,1962,1261,719,128,256,1774,3826,

%U 6604,12349,6604,3826,1774,256,512,4389,11770,22446,66149,66149,22446,11770

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1....2.....4......8......16........32.........64..........128...........256

%C ...2....8....21.....49.....120.......293........719.........1774..........4389

%C ...4...21....45....142.....439......1261.......3826........11770.........35152

%C ...8...49...142....458....1962......6604......22446........86464........311891

%C ..16..120...439...1962...12349.....66149.....321707......1803281.......9990733

%C ..32..293..1261...6604...66149....554682....3914486.....34263459.....301965791

%C ..64..719..3826..22446..321707...3914486...36596835....458669749....5842600934

%C .128.1774.11770..86464.1803281..34263459..458669749...8395262149..162463649507

%C .256.4389.35152.311891.9990733.301965791.5842600934.162463649507.4973359586800

%H R. H. Hardin, <a href="/A306053/b306053.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

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

%F k=3: [order 10] for n>12

%F k=4: [order 21] for n>25

%F k=5: [order 85] for n>89

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303721.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 18 2018