A317697 - OEIS

%I #4 Aug 04 2018 20:11:10

%S 1,2,2,3,5,3,5,9,9,5,8,21,14,21,8,13,57,33,33,57,13,21,125,92,141,92,

%T 125,21,34,289,220,630,630,220,289,34,55,741,593,2742,6984,2742,593,

%U 741,55,89,1737,1787,16008,45681,45681,16008,1787,1737,89,144,4045,5401,100830

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..1....2....3......5........8.........13...........21..............34

%C ..2....5....9.....21.......57........125..........289.............741

%C ..3....9...14.....33.......92........220..........593............1787

%C ..5...21...33....141......630.......2742........16008..........100830

%C ..8...57...92....630.....6984......45681.......464357.........6124074

%C .13..125..220...2742....45681.....585418.....12414382.......278773058

%C .21..289..593..16008...464357...12414382....526480617.....21681685596

%C .34..741.1787.100830..6124074..278773058..21681685596...1721401739325

%C .55.1737.5401.603699.64822432.5491231349.800622189621.116191191089274

%H R. H. Hardin, <a href="/A317697/b317697.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) = 2*a(n-1) -a(n-2) +8*a(n-3) -8*a(n-4)

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

%F k=4: [order 52] for n>55

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304349.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 04 2018