A317902 - OEIS

%I #4 Aug 10 2018 10:41:02

%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,4,3,3,4,0,0,9,2,13,2,9,0,0,22,4,31,

%T 31,4,22,0,0,53,6,54,29,54,6,53,0,0,130,14,116,75,75,116,14,130,0,0,

%U 320,14,342,315,167,315,342,14,320,0,0,788,22,956,708,502,502,708,956,22,788,0

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

%C Table starts

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

%C .0...1..1...2....4....9....22.....53....130.....320.....788.....1942.....4787

%C .0...1..1...3....2....4.....6.....14.....14......22......43.......68.......82

%C .0...2..3..13...31...54...116....342....956....2459....6366....16404....42964

%C .0...4..2..31...29...75...315....708...1978....4962...13865....38184...101161

%C .0...9..4..54...75..167...502...2064...5877...17008...53512...175313...540037

%C .0..22..6.116..315..502..3630...7770..34645...86317..320622...966922..3306875

%C .0..53.14.342..708.2064..7770..38448.114588..399679.1493075..5351225.18918592

%C .0.130.14.956.1978.5877.34645.114588.534829.1600960.7124145.24417579.99555342

%H R. H. Hardin, <a href="/A317902/b317902.txt">Table of n, a(n) for n = 1..364</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 10] for n>13

%F k=4: [order 30] for n>34

%F k=5: [order 61] for n>69

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A317735.

%Y Column 3 is A317736.

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Aug 10 2018