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A299554 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 0,0,0,0,1,0,0,3,3,0,0,6,9,6,0,0,17,31,31,17,0,0,41,166,220,166,41,0,

%T 0,104,752,2034,2034,752,104,0,0,261,3739,17565,37283,17565,3739,261,

%U 0,0,655,18300,160089,621694,621694,160089,18300,655,0,0,1646,90313,1456436

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0...0.....0........0..........0............0...............0.................0

%C .0...1.....3........6.........17...........41.............104...............261

%C .0...3.....9.......31........166..........752............3739.............18300

%C .0...6....31......220.......2034........17565..........160089...........1456436

%C .0..17...166.....2034......37283.......621694........10759709.........186196755

%C .0..41...752....17565.....621694.....19604624.......648002718.......21337630973

%C .0.104..3739...160089...10759709....648002718.....40708113490.....2548695927399

%C .0.261.18300..1456436..186196755..21337630973...2548695927399...303433045764806

%C .0.655.90313.13302816.3228302388.704140369456.159913303887571.36196880526512847

%H R. H. Hardin, <a href="/A299554/b299554.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) = a(n-1) +3*a(n-2) +2*a(n-3)

%F k=3: [order 13] for n>15

%F k=4: [order 37] for n>38

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A297972.

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Feb 12 2018

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Last modified August 10 10:09 EDT 2022. Contains 356039 sequences. (Running on oeis4.)