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%I #4 Aug 09 2018 09:47:23
%S 0,1,1,1,3,1,2,6,6,2,3,10,4,10,3,5,21,19,19,21,5,8,46,32,56,32,46,8,
%T 13,102,72,155,155,72,102,13,21,220,164,313,350,313,164,220,21,34,491,
%U 331,851,1001,1001,851,331,491,34,55,1077,790,2147,2616,3315,2616,2147,790
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C Table starts
%C ..0...1...1....2.....3.....5......8......13......21.......34........55
%C ..1...3...6...10....21....46....102.....220.....491.....1077......2393
%C ..1...6...4...19....32....72....164.....331.....790.....1700......3879
%C ..2..10..19...56...155...313....851....2147....5513....14288.....37168
%C ..3..21..32..155...350..1001...2616....7926...21882....65134....190018
%C ..5..46..72..313..1001..3315...9045...28091...87900...278545....886735
%C ..8.102.164..851..2616..9045..33238..116271..405766..1489264...5416535
%C .13.220.331.2147..7926.28091.116271..517734.1946626..8076505..33329441
%C .21.491.790.5513.21882.87900.405766.1946626.8875636.40432932.186507496
%H R. H. Hardin, <a href="/A317863/b317863.txt">Table of n, a(n) for n = 1..264</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) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)
%F k=3: [order 26] for n>32
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..0..1. .0..0..0..1. .0..1..1..1. .0..1..0..1
%e ..1..1..0..0. .1..1..1..0. .1..0..1..1. .1..0..0..1. .1..1..1..0
%e ..0..1..1..0. .1..1..1..1. .0..0..0..1. .1..0..1..0. .0..1..1..1
%e ..1..1..0..0. .0..1..1..0. .1..0..1..0. .1..1..0..0. .1..1..1..1
%e ..1..0..0..1. .1..0..1..1. .0..0..1..1. .0..0..0..1. .0..0..0..0
%Y Column 1 is A000045(n-1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Aug 09 2018
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