A304427 - OEIS

%I #4 May 12 2018 09:39:02

%S 0,1,1,1,7,1,2,25,25,2,3,98,124,98,3,5,383,836,836,383,5,8,1493,5227,

%T 9304,5227,1493,8,13,5824,33263,98190,98190,33263,5824,13,21,22717,

%U 210954,1043316,1712347,1043316,210954,22717,21,34,88609,1338995

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ..1.....7......25.........98..........383...........1493.............5824

%C ..1....25.....124........836.........5227..........33263...........210954

%C ..2....98.....836.......9304........98190........1043316.........11085965

%C ..3...383....5227......98190......1712347.......30362267........536823135

%C ..5..1493...33263....1043316.....30362267......898146670......26510744474

%C ..8..5824..210954...11085965....536823135....26510744474....1305482386171

%C .13.22717.1338995..117776344...9501018264...783174010085...64363459841666

%C .21.88609.8497693.1251440091.168137854364.23137703330738.3173399640697899

%H R. H. Hardin, <a href="/A304427/b304427.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) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

%F k=3: [order 9] for n>10

%F k=4: [order 27] for n>28

%F k=5: [order 90] for n>93

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 12 2018