A304704 - OEIS

%I #4 May 17 2018 10:03:54

%S 0,1,1,1,3,1,2,11,11,2,3,10,8,10,3,5,51,21,21,51,5,8,165,46,48,46,165,

%T 8,13,306,103,215,215,103,306,13,21,993,201,798,908,798,201,993,21,34,

%U 2867,512,3055,5232,5232,3055,512,2867,34,55,6818,1123,9810,19701,47440,19701

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

%C Table starts

%C ..0....1....1.....2......3........5.........8..........13...........21

%C ..1....3...11....10.....51......165.......306.........993.........2867

%C ..1...11....8....21.....46......103.......201.........512.........1123

%C ..2...10...21....48....215......798......3055........9810........41744

%C ..3...51...46...215....908.....5232.....19701......135455.......872954

%C ..5..165..103...798...5232....47440....296646.....2733069.....26024851

%C ..8..306..201..3055..19701...296646...3510334....37931518....611105804

%C .13..993..512..9810.135455..2733069..37931518...799135415..19924071081

%C .21.2867.1123.41744.872954.26024851.611105804.19924071081.758781064050

%H R. H. Hardin, <a href="/A304704/b304704.txt">Table of n, a(n) for n = 1..180</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>20

%F k=4: [order 67] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304052.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 17 2018