A304604 - OEIS

%I #4 May 15 2018 13:31:52

%S 1,2,2,4,4,4,8,5,5,8,16,9,13,9,16,32,22,23,23,22,32,64,45,53,73,53,45,

%T 64,128,101,131,179,179,131,101,128,256,218,330,515,560,515,330,218,

%U 256,512,477,793,1450,1726,1726,1450,793,477,512,1024,1041,1930,4024,5205,6007

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 6 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1...2....4.....8....16.....32......64......128......256.......512.......1024

%C ...2...4....5.....9....22.....45.....101......218......477......1041.......2270

%C ...4...5...13....23....53....131.....330......793.....1930......4765......11686

%C ...8...9...23....73...179....515....1450.....4024....11122.....31092......86816

%C ..16..22...53...179...560...1726....5205....15474....46577....140882.....425811

%C ..32..45..131...515..1726...6007...19634....66861...231749....813171....2823452

%C ..64.101..330..1450..5205..19634...75463...317420..1356754...5638479...22732759

%C .128.218..793..4024.15474..66861..317420..1874284.10089904..49126115..230760262

%C .256.477.1930.11122.46577.231749.1356754.10089904.62934491.341047788.1822167540

%H R. H. Hardin, <a href="/A304604/b304604.txt">Table of n, a(n) for n = 1..337</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +2*a(n-4) -2*a(n-5) -7*a(n-6) -6*a(n-7) for n>10

%F k=4: [order 17] for n>22

%F k=5: [order 33] for n>39

%F k=6: [order 92] for n>99

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A052962 for n>2.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, May 15 2018