A316176 - OEIS

%I #4 Jun 25 2018 17:40:45

%S 0,1,1,1,3,1,2,11,11,2,3,10,16,10,3,5,51,34,34,51,5,8,165,113,72,113,

%T 165,8,13,306,275,331,331,275,306,13,21,993,604,1425,3087,1425,604,

%U 993,21,34,2867,1804,5297,16382,16382,5297,1804,2867,34,55,6818,4683,18573,66575

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6 or 7 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...16....34.....113.......275........604.........1804..........4683

%C ..2...10...34....72.....331......1425.......5297........18573.........84658

%C ..3...51..113...331....3087.....16382......66575.......500251.......3416740

%C ..5..165..275..1425...16382....139293.....976178.....10070845.....106916450

%C ..8..306..604..5297...66575....976178...12236682....164577403....2930093529

%C .13..993.1804.18573..500251..10070845..164577403...4139589568..113829450853

%C .21.2867.4683.84658.3416740.106916450.2930093529.113829450853.4957413596069

%H R. H. Hardin, <a href="/A316176/b316176.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 18] for n>20

%F k=4: [order 64] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304052.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jun 25 2018