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A296827 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 3 or 4 king-move neighboring 1s. 8

%I

%S 1,1,1,1,6,1,1,21,21,1,1,56,94,56,1,1,178,352,352,178,1,1,609,2133,

%T 2272,2133,609,1,1,1997,11930,24367,24367,11930,1997,1,1,6511,60772,

%U 214243,510086,214243,60772,6511,1,1,21494,326592,1814475,8721984,8721984

%N T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 2, 3 or 4 king-move neighboring 1s.

%C Table starts

%C .1.....1.......1.........1...........1.............1................1

%C .1.....6......21........56.........178...........609.............1997

%C .1....21......94.......352........2133.........11930............60772

%C .1....56.....352......2272.......24367........214243..........1814475

%C .1...178....2133.....24367......510086.......8721984........139963008

%C .1...609...11930....214243.....8721984.....267542809.......7478283799

%C .1..1997...60772...1814475...139963008....7478283799.....364592446431

%C .1..6511..326592..16388418..2411616295..232289837440...20210620228470

%C .1.21494.1772900.145662798.41118326040.7106285417721.1091459884529060

%H R. H. Hardin, <a href="/A296827/b296827.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +5*a(n-3) -2*a(n-4) -10*a(n-5) -8*a(n-6)

%F k=3: [order 16]

%F k=4: [order 35]

%e Some solutions for n=4 k=4

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Dec 21 2017

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Last modified January 20 08:12 EST 2021. Contains 340301 sequences. (Running on oeis4.)