A299089 - OEIS

%I #4 Feb 02 2018 08:06:30

%S 1,2,2,4,8,4,8,26,26,8,16,88,92,88,16,32,298,354,354,298,32,64,1012,

%T 1387,1617,1387,1012,64,128,3440,5470,7722,7722,5470,3440,128,256,

%U 11700,21484,36667,46456,36667,21484,11700,256,512,39804,84425,173524,273360,273360

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

%C Table starts

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

%C ...2.....8.....26......88......298......1012........3440........11700

%C ...4....26.....92.....354.....1387......5470.......21484........84425

%C ...8....88....354....1617.....7722.....36667......173524.......822065

%C ..16...298...1387....7722....46456....273360.....1598956......9400094

%C ..32..1012...5470...36667...273360...2001653....14514670....105596164

%C ..64..3440..21484..173524..1598956..14514670...129999453...1166134994

%C .128.11700..84425..822065..9400094.105596164..1166134994..12899638332

%C .256.39804.331838.3897261.55296169.769538056.10493701031.143316205219

%H R. H. Hardin, <a href="/A299089/b299089.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) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5)

%F k=3: [order 17] for n>19

%F k=4: [order 64] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A298189.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 02 2018