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 A316311 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 6 or 8 king-move adjacent elements, with upper left element zero. 7

%I

%S 1,2,2,3,5,3,5,7,7,5,8,17,10,17,8,13,35,21,21,35,13,21,61,44,74,44,61,

%T 21,34,127,83,148,148,83,127,34,55,265,168,404,662,404,168,265,55,89,

%U 507,365,1046,1488,1488,1046,365,507,89,144,1013,766,3023,4583,4431,4583

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

%C Table starts

%C ..1...2...3....5.....8.....13......21.......34........55.........89.........144

%C ..2...5...7...17....35.....61.....127......265.......507.......1013........2071

%C ..3...7..10...21....44.....83.....168......365.......766.......1615........3490

%C ..5..17..21...74...148....404....1046.....3023......8295......24149.......72052

%C ..8..35..44..148...662...1488....4583....18558.....56204.....188141......712440

%C .13..61..83..404..1488...4431...17487....75221....293206....1262596.....5656690

%C .21.127.168.1046..4583..17487...96175...534083...2689151...15357780....89959730

%C .34.265.365.3023.18558..75221..534083..3854852..23640130..172324121..1280488352

%C .55.507.766.8295.56204.293206.2689151.23640130.190235425.1767871577.16603983388

%H R. H. Hardin, <a href="/A316311/b316311.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) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

%F k=3: [order 16]

%F k=4: [order 67] for n>68

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+1).

%Y Column 2 is A303802.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jun 29 2018

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Last modified February 7 12:58 EST 2023. Contains 360123 sequences. (Running on oeis4.)