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%I #6 Mar 10 2022 20:46:59
%S 1,2,2,3,4,3,5,3,3,5,8,13,3,13,8,13,34,9,9,34,13,21,73,17,63,17,73,21,
%T 34,203,48,119,119,48,203,34,55,594,94,243,507,243,94,594,55,89,1443,
%U 234,1086,934,934,1086,234,1443,89,144,4013,589,2782,6236,2466,6236,2782,589
%N T(n,k) = Number of n X k 0..1 arrays with every element equal to 0, 1, 3, 4 or 6 king-move adjacent elements, with upper left element zero.
%C Table starts
%C ..1....2...3....5......8.....13......21.......34........55.........89
%C ..2....4...3...13.....34.....73.....203......594......1443.......4013
%C ..3....3...3....9.....17.....48......94......234.......589.......1333
%C ..5...13...9...63....119....243....1086.....2782......8509......31229
%C ..8...34..17..119....507....934....6236....28894....110488.....622009
%C .13...73..48..243....934...2466...11175....48002....249672....1256472
%C .21..203..94.1086...6236..11175..111137...644056...3190955...27151266
%C .34..594.234.2782..28894..48002..644056..5833295..35487422..441894670
%C .55.1443.589.8509.110488.249672.3190955.35487422.281897638.3673383638
%H R. H. Hardin, <a href="/A298320/b298320.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1) +a(n-2).
%F k=2: a(n) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6.
%F k=3: [order 17] for n>18.
%F k=4: [order 71] for n>72.
%e Some solutions for n=7, k=4
%e ..0..1..0..1. .0..1..1..0. .0..0..1..1. .0..1..0..1. .0..1..1..0
%e ..0..1..0..1. .1..1..0..1. .0..0..1..1. .1..1..1..0. .1..1..0..1
%e ..1..1..1..1. .0..1..0..0. .1..0..1..0. .0..1..0..0. .0..1..0..0
%e ..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e ..1..1..1..0. .1..1..0..0. .0..0..1..1. .1..1..0..1. .0..0..0..1
%e ..0..1..0..0. .1..1..1..0. .0..0..0..1. .0..1..0..0. .0..1..0..0
%e ..1..0..0..1. .0..1..1..0. .1..0..0..1. .1..0..0..1. .1..0..0..0
%Y Column 1 is A000045(n+1).
%Y Column 2 is A297901.
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Jan 17 2018
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