|
%I #4 Jun 28 2018 15:26:05
%S 0,1,1,1,7,1,2,25,25,2,3,98,125,98,3,5,383,846,846,383,5,8,1493,5321,
%T 9540,5321,1493,8,13,5824,34017,102072,102072,34017,5824,13,21,22717,
%U 216805,1099200,1820908,1099200,216805,22717,21,34,88609,1382759
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 8 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.....125........846.........5321..........34017...........216805
%C ..2....98.....846.......9540.......102072........1099200.........11834419
%C ..3...383....5321.....102072......1820908.......32932624........594230641
%C ..5..1493...34017....1099200.....32932624.....1000914270......30350372014
%C ..8..5824..216805...11834419....594230641....30350372014....1545539179382
%C .13.22717.1382759..127394654..10728510594...920820679433...78766985363848
%C .21.88609.8818011.1371525369.193678113501.27936246990475.4013958393240781
%H R. H. Hardin, <a href="/A316282/b316282.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 95] for n>97
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..0..1..0. .0..0..0..1
%e ..0..1..0..0. .1..0..1..0. .0..0..0..1. .1..1..1..1. .0..1..1..0
%e ..1..1..0..1. .0..1..1..1. .0..1..1..0. .0..0..1..0. .1..1..0..1
%e ..1..1..0..0. .1..0..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0
%e ..0..0..1..0. .1..0..0..1. .1..0..1..1. .1..1..1..1. .0..1..1..0
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304421.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 28 2018
| 