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A298667 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero. 7

%I

%S 1,1,1,1,1,1,1,0,0,1,1,1,3,1,1,1,2,1,1,2,1,1,1,5,2,5,1,1,1,8,8,2,2,8,

%T 8,1,1,5,7,9,20,9,7,5,1,1,22,25,13,38,38,13,25,22,1,1,29,25,26,84,169,

%U 84,26,25,29,1,1,60,58,74,319,238,238,319,74,58,60,1,1,121,95,134,770,1019,978

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

%C Table starts

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

%C .1..1..0..1...2....1.....8.....5.....22......29......60......121.......194

%C .1..0..3..1...5....8.....7....25.....25......58......95......155.......299

%C .1..1..1..2...2....9....13....26.....74.....134.....325......731......1568

%C .1..2..5..2..20...38....84...319....770....2106....6301....17282.....47774

%C .1..1..8..9..38..169...238..1019...3112....7518...25887....74736....218787

%C .1..8..7.13..84..238...978..3895..11843...49752..184380...640323...2550161

%C .1..5.25.26.319.1019..3895.22938..81474..386923.1791871..7595552..35648606

%C .1.22.25.74.770.3112.11843.81474.329249.1693779.9364144.43238329.235861179

%H R. H. Hardin, <a href="/A298667/b298667.txt">Table of n, a(n) for n = 1..241</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) for n>5

%F k=3: [order 12]

%F k=4: [order 35]

%e Some solutions for n=8 k=4

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

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

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

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

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

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

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

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

%Y Column 2 is A297809(n-2).

%K nonn,tabl

%O 1,13

%A _R. H. Hardin_, Jan 24 2018

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Last modified June 22 18:49 EDT 2021. Contains 345388 sequences. (Running on oeis4.)