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A297094 T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 3 king-move neighboring 1s. 8

%I

%S 2,4,4,8,15,8,16,45,45,16,32,152,228,152,32,64,511,1256,1256,511,64,

%T 128,1681,6859,11925,6859,1681,128,256,5588,37423,113084,113084,37423,

%U 5588,256,512,18575,204625,1060921,1850693,1060921,204625,18575,512,1024

%N T(n,k)=Number of nXk 0..1 arrays with no 1 adjacent to 3 king-move neighboring 1s.

%C Table starts

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

%C ...4....15......45.......152..........511...........1681.............5588

%C ...8....45.....228......1256.........6859..........37423...........204625

%C ..16...152....1256.....11925.......113084........1060921.........10038612

%C ..32...511....6859....113084......1850693.......30151640........497994853

%C ..64..1681...37423...1060921.....30151640......859032804......24929815289

%C .128..5588..204625..10038612....497994853....24929815289....1280846320436

%C .256.18575.1118722..95094637...8248067202...728501800356...66546097409172

%C .512.61621.6116809.900615714.136768286476.21357821717826.3477139838772757

%H R. H. Hardin, <a href="/A297094/b297094.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) +3*a(n-3) -14*a(n-4) +4*a(n-5)

%F k=3: [order 19]

%F k=4: [order 42]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 25 2017

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)