A318423 - OEIS

%I #4 Aug 26 2018 11:16:28

%S 1,1,1,1,2,1,1,2,2,1,1,3,2,3,1,1,5,4,4,5,1,1,10,5,18,5,10,1,1,23,8,71,

%T 71,8,23,1,1,54,9,126,129,126,9,54,1,1,131,28,225,280,280,225,28,131,

%U 1,1,321,44,691,839,783,839,691,44,321,1,1,789,60,2116,2717,2489,2489,2717

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

%C Table starts

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

%C .1...2..2....3....5....10.....23......54.....131......321.......789......1943

%C .1...2..2....4....5.....8......9......28......44.......60.......118.......256

%C .1...3..4...18...71...126....225.....691....2116.....6101.....15907.....40782

%C .1...5..5...71..129...280....839....2717....8803....25414.....74518....227494

%C .1..10..8..126..280...783...2489....9381...35283...124358....433497...1542555

%C .1..23..9..225..839..2489..11802...45560..190929...738777...2951001..11787988

%C .1..54.28..691.2717..9381..45560..236755.1089386..4911132..22619361.104787816

%C .1.131.44.2116.8803.35283.190929.1089386.5897333.30194599.159545175.842177622

%H R. H. Hardin, <a href="/A318423/b318423.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

%F k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) -a(n-6)

%F k=3: [order 17] for n>19

%F k=4: [order 58] for n>62

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A317809.

%Y Column 3 is A317810.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Aug 26 2018