A300465 - OEIS

%I #4 Mar 06 2018 11:29:53

%S 0,0,0,0,1,0,0,2,2,0,0,4,2,4,0,0,9,8,8,9,0,0,19,22,28,22,19,0,0,41,68,

%T 142,142,68,41,0,0,88,212,540,1146,540,212,88,0,0,189,652,2585,7456,

%U 7456,2585,652,189,0,0,406,2017,11343,55663,78195,55663,11343,2017,406,0,0

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

%C .0...1....2.....4.......9........19.........41...........88............189

%C .0...2....2.....8......22........68........212..........652...........2017

%C .0...4....8....28.....142.......540.......2585........11343..........51501

%C .0...9...22...142....1146......7456......55663.......400028........2906875

%C .0..19...68...540....7456.....78195.....935121.....10913850......127028268

%C .0..41..212..2585...55663....935121...17675111....330639367.....6123205255

%C .0..88..652.11343..400028..10913850..330639367...9829599051...293961266876

%C .0.189.2017.51501.2906875.127028268.6123205255.293961266876.14061129641181

%H R. H. Hardin, <a href="/A300465/b300465.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

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

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

%F k=3: [order 15]

%F k=4: [order 52] for n>54

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A078039(n-2).

%K nonn,tabl

%O 1,8

%A _R. H. Hardin_, Mar 06 2018