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A282316 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than four of its king-move neighbors. 8

%I

%S 2,4,4,8,16,8,16,63,63,16,32,249,419,249,32,64,984,2968,2968,984,64,

%T 128,3888,21055,40024,21055,3888,128,256,15363,148793,535494,535494,

%U 148793,15363,256,512,60705,1052672,7114808,13473987,7114808,1052672,60705,512

%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than four of its king-move neighbors.

%C Table starts

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

%C ....4.....16........63..........249.............984..............3888

%C ....8.....63.......419.........2968...........21055............148793

%C ...16....249......2968........40024..........535494...........7114808

%C ...32....984.....21055.......535494........13473987.........335154112

%C ...64...3888....148793......7114808.......335154112.......15544631618

%C ..128..15363...1052672.....94872444......8386104536......726938227646

%C ..256..60705...7447859...1264480188....209686247202....33959500217027

%C ..512.239868..52689903..16850046438...5240914986790..1585545530659659

%C .1024.947808.372763688.224565308124.131022200932324.74053519870574822

%H R. H. Hardin, <a href="/A282316/b282316.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) +3*a(n-2) +3*a(n-3)

%F k=3: [order 10]

%F k=4: [order 18]

%F k=5: [order 57]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Feb 11 2017

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Last modified May 25 13:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)