A299844 - OEIS

%I #4 Feb 20 2018 08:24:36

%S 1,2,2,4,8,4,8,31,31,8,16,121,163,121,16,32,472,927,927,472,32,64,

%T 1841,5331,8245,5331,1841,64,128,7181,30535,74329,74329,30535,7181,

%U 128,256,28010,175286,664377,1056001,664377,175286,28010,256,512,109255,1006611

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ...2......8......31.......121.........472..........1841............7181

%C ...4.....31.....163.......927........5331.........30535..........175286

%C ...8....121.....927......8245.......74329........664377.........5966905

%C ..16....472....5331.....74329.....1056001......14831535.......209649848

%C ..32...1841...30535....664377....14831535.....325878154......7216925214

%C ..64...7181..175286...5966905...209649848....7216925214....250915415042

%C .128..28010.1006611..53667656..2971226455..160460196001...8769920586285

%C .256.109255.5780036.482603686.42097006186.3565906147902.306309096924610

%H R. H. Hardin, <a href="/A299844/b299844.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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

%F k=3: [order 10] for n>11

%F k=4: [order 30] for n>31

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A281831.

%Y Column 3 is A299076.

%Y Column 4 is A299077.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 20 2018