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%I #4 Feb 20 2016 09:46:22
%S 4,16,16,60,108,60,216,708,708,216,756,4476,9284,4476,756,2592,27684,
%T 115452,115452,27684,2592,8748,168252,1399612,2817548,1399612,168252,
%U 8748,29160,1008804,16629436,67134380,67134380,16629436,1008804,29160
%N T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling three no more than once.
%C Table starts
%C ......4........16...........60.............216................756
%C .....16.......108..........708............4476..............27684
%C .....60.......708.........9284..........115452............1399612
%C ....216......4476.......115452.........2817548...........67134380
%C ....756.....27684......1399612........67134380.........3159954052
%C ...2592....168252.....16629436......1567933676.......145995171708
%C ...8748...1008804....194596516.....36068275268......6648192704604
%C ..29160...5983164...2249848972....819789099172....299224791093196
%C ..96228..35170980..25758552060..18452018423420..13339889117822420
%C .314928.205214268.292530733516.411983259384452.590022908205332548
%H R. H. Hardin, <a href="/A269194/b269194.txt">Table of n, a(n) for n = 1..219</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F k=2: a(n) = 10*a(n-1) -21*a(n-2) -20*a(n-3) -4*a(n-4) for n>5
%F k=3: [order 8] for n>9
%F k=4: [order 16] for n>17
%F k=5: [order 40] for n>41
%e Some solutions for n=3 k=4
%e ..0..1..1..3. .0..0..2..2. .2..3..1..3. .1..3..1..1. .2..3..2..1
%e ..0..1..3..1. .2..0..0..2. .2..3..1..3. .1..1..1..3. .2..2..3..3
%e ..1..3..1..1. .2..0..2..0. .3..3..1..0. .0..3..1..3. .3..2..3..2
%Y Column 1 is A120926(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 20 2016