A305182 - OEIS

%I #4 May 26 2018 18:39:22

%S 0,1,1,1,3,1,2,2,2,2,3,1,8,1,3,5,8,9,9,8,5,8,5,14,10,14,5,8,13,22,29,

%T 13,13,29,22,13,21,29,49,47,64,47,49,29,21,34,60,78,71,137,137,71,78,

%U 60,34,55,121,135,118,140,473,140,118,135,121,55,89,194,245,241,668,836,836

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0..1...1...2....3....5.....8....13.....21......34......55.......89......144

%C ..1..3...2...1....8....5....22....29.....60.....121.....194......425......704

%C ..1..2...8...9...14...29....49....78....135.....245.....406......683.....1197

%C ..2..1...9..10...13...47....71...118....241.....453.....870.....1608.....3110

%C ..3..8..14..13...64..137...140...668...1652....2361....6578....18378....34712

%C ..5..5..29..47..137..473...836..2109...6105...13157...29710....79848...188417

%C ..8.22..49..71..140..836..1750..5407..19965...44251..150549...488420..1217938

%C .13.29..78.118..668.2109..5407.24506..88179..249772.1002134..3694424.11389401

%C .21.60.135.241.1652.6105.19965.88179.370094.1271336.5213917.22257523.80767363

%H R. H. Hardin, <a href="/A305182/b305182.txt">Table of n, a(n) for n = 1..312</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-2) +2*a(n-3) -2*a(n-4) for n>6

%F k=3: a(n) = 4*a(n-3) +4*a(n-4) -a(n-6) -8*a(n-7) -2*a(n-9) -4*a(n-10) for n>13

%F k=4: [order 11] for n>18

%F k=5: [order 43] for n>50

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A297809 for n>2.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 26 2018