A316304 - OEIS

%I #4 Jun 29 2018 07:14:53

%S 1,2,2,4,4,4,8,12,12,8,16,24,20,24,16,32,64,39,39,64,32,64,184,110,

%T 114,110,184,64,128,432,245,339,339,245,432,128,256,1088,572,1021,

%U 1519,1021,572,1088,256,512,2944,1384,2929,5120,5120,2929,1384,2944,512,1024,7360

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

%C Table starts

%C ...1....2....4.....8.....16......32.......64.......128........256.........512

%C ...2....4...12....24.....64.....184......432......1088.......2944........7360

%C ...4...12...20....39....110.....245......572......1384.......3267........7767

%C ...8...24...39...114....339....1021.....2929......8639......25410.......74617

%C ..16...64..110...339...1519....5120....19185.....72289.....268933......999260

%C ..32..184..245..1021...5120...20780....97864....444290....2065314.....9512624

%C ..64..432..572..2929..19185...97864...608947...3605691...21632912...130126938

%C .128.1088.1384..8639..72289..444290..3605691..26898537..208808616..1617004105

%C .256.2944.3267.25410.268933.2065314.21632912.208808616.2095245767.21106046766

%H R. H. Hardin, <a href="/A316304/b316304.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) = 2*a(n-1) +8*a(n-3) -8*a(n-4) -8*a(n-5) for n>6

%F k=3: [order 12] for n>13

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

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A303794.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 29 2018