A317458 - OEIS

%I #4 Jul 28 2018 20:54:04

%S 0,1,1,1,3,1,2,11,11,2,3,10,17,10,3,5,51,36,36,51,5,8,165,131,72,131,

%T 165,8,13,306,322,353,353,322,306,13,21,993,762,1525,4364,1525,762,

%U 993,21,34,2867,2337,5601,21250,21250,5601,2337,2867,34,55,6818,6165,20603,95144

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0....1....1.....2.......3.........5..........8...........13............21

%C ..1....3...11....10......51.......165........306..........993..........2867

%C ..1...11...17....36.....131.......322........762.........2337..........6165

%C ..2...10...36....72.....353......1525.......5601........20603.........93180

%C ..3...51..131...353....4364.....21250......95144.......744225.......4783771

%C ..5..165..322..1525...21250....165890....1201543.....12609827.....130759485

%C ..8..306..762..5601...95144...1201543...14872138....206130149....3590280962

%C .13..993.2337.20603..744225..12609827..206130149...5301169782..141656940788

%C .21.2867.6165.93180.4783771.130759485.3590280962.141656940788.6077202952491

%H R. H. Hardin, <a href="/A317458/b317458.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) = a(n-1) +3*a(n-2) +8*a(n-3) -4*a(n-4) -16*a(n-5) for n>6

%F k=3: [order 18] for n>20

%F k=4: [order 64] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A304052.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 28 2018