|
%I #4 Aug 05 2018 15:51:13
%S 0,1,1,1,7,1,2,25,25,2,3,98,161,98,3,5,383,1250,1250,383,5,8,1493,
%T 9541,19208,9541,1493,8,13,5824,72715,293378,293378,72715,5824,13,21,
%U 22717,554642,4458098,8931649,4458098,554642,22717,21,34,88609,4229957
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 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
%C ..1.....7.......25..........98...........383.............1493
%C ..1....25......161........1250..........9541............72715
%C ..2....98.....1250.......19208........293378..........4458098
%C ..3...383.....9541......293378.......8931649........270714329
%C ..5..1493....72715.....4458098.....270714329......16360102553
%C ..8..5824...554642....67837952....8216055128.....990049380944
%C .13.22717..4229957..1032124178..249314217853...59904290609773
%C .21.88609.32260015.15703109762.7565327218559.3624564255839937
%H R. H. Hardin, <a href="/A317733/b317733.txt">Table of n, a(n) for n = 1..364</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: a(n) = 6*a(n-1) +11*a(n-2) +11*a(n-3) -2*a(n-4) -a(n-5) -2*a(n-6)
%F k=4: a(n) = 12*a(n-1) +42*a(n-2) +107*a(n-3) -30*a(n-4) +12*a(n-5) -16*a(n-6)
%F k=5: [order 21]
%F k=6: [order 36]
%F k=7: [order 81]
%e Some solutions for n=5 k=4
%e ..0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..1..0. .0..0..0..0
%e ..1..0..1..0. .1..1..0..0. .1..1..1..1. .1..1..0..0. .0..1..1..1
%e ..1..1..1..0. .0..0..1..1. .0..0..0..0. .0..0..0..0. .1..1..1..1
%e ..1..0..1..1. .1..0..0..1. .1..0..0..1. .0..1..1..0. .1..0..0..0
%e ..1..1..0..1. .1..0..1..1. .1..0..0..0. .0..1..1..0. .0..1..0..1
%Y Column 1 is A000045(n-1).
%Y Column 2 is A304421.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Aug 05 2018
| 