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A304156 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3, 4 or 6 king-move adjacent elements, with upper left element zero. 7

%I #4 May 07 2018 09:04:46

%S 0,0,0,0,3,0,0,5,5,0,0,18,4,18,0,0,61,42,42,61,0,0,209,130,346,130,

%T 209,0,0,702,464,1767,1767,464,702,0,0,2381,1722,10182,13279,10182,

%U 1722,2381,0,0,8069,6378,60352,100942,100942,60352,6378,8069,0,0,27330,22939,350540

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

%C Table starts

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

%C .0....3.....5......18.......61........209.........702..........2381

%C .0....5.....4......42......130........464........1722..........6378

%C .0...18....42.....346.....1767......10182.......60352........350540

%C .0...61...130....1767....13279.....100942......839935.......6803634

%C .0..209...464...10182...100942....1100030....12806826.....145611915

%C .0..702..1722...60352...839935...12806826...217640633....3520683600

%C .0.2381..6378..350540..6803634..145611915..3520683600...80851458613

%C .0.8069.22939.2034140.54261600.1634366796.56360283031.1830588080314

%H R. H. Hardin, <a href="/A304156/b304156.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) = 3*a(n-1) +a(n-2) +2*a(n-3) -2*a(n-4) -4*a(n-5) for n>6

%F k=3: [order 18] for n>19

%F k=4: [order 66] for n>67

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A303684.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 07 2018

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Last modified July 15 01:36 EDT 2024. Contains 374323 sequences. (Running on oeis4.)