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%I #4 Feb 21 2016 09:27:23
%S 4,16,16,60,216,64,216,2124,2592,256,756,19188,62748,29160,1024,2592,
%T 164556,1363572,1698732,314928,4096,8748,1363572,27788292,87559668,
%U 43674876,3306744,16384,29160,11026764,544118148,4204943820,5306911092
%N T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than once.
%C Table starts
%C ......4.........16.............60...............216...................756
%C .....16........216...........2124.............19188................164556
%C .....64.......2592..........62748...........1363572..............27788292
%C ....256......29160........1698732..........87559668............4204943820
%C ...1024.....314928.......43674876........5306911092..........598478857956
%C ...4096....3306744.....1085203980......309846524148........81907569617580
%C ..16384...34012224....26317946844....17623065834612.....10908770041709316
%C ..65536..344373768...626778812268...983118947312628...1424067311317705740
%C .262144.3443737680.14718495557052.54032675767734132.183070424003703987492
%H R. H. Hardin, <a href="/A269289/b269289.txt">Table of n, a(n) for n = 1..241</a>
%F Empirical for column k:
%F k=1: a(n) = 4*a(n-1)
%F k=2: a(n) = 18*a(n-1) -81*a(n-2)
%F k=3: a(n) = 42*a(n-1) -441*a(n-2)
%F k=4: a(n) = 98*a(n-1) -2401*a(n-2) for n>3
%F k=5: a(n) = 234*a(n-1) -14277*a(n-2) +68796*a(n-3) -86436*a(n-4)
%F k=6: [order 6] for n>7
%F k=7: [order 10] for n>11
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -9*a(n-2)
%F n=2: a(n) = 14*a(n-1) -49*a(n-2) for n>4
%F n=3: a(n) = 36*a(n-1) -378*a(n-2) +972*a(n-3) -729*a(n-4) for n>7
%F n=4: [order 8] for n>12
%F n=5: [order 18] for n>23
%F n=6: [order 40] for n>46
%e Some solutions for n=3 k=4
%e ..0..2..3..3. .0..2..3..1. .0..0..0..1. .0..2..2..2. .2..0..0..2
%e ..2..1..3..1. .2..1..0..2. .2..2..3..1. .0..2..0..0. .0..0..3..3
%e ..3..1..0..1. .1..0..2..0. .1..3..3..3. .2..0..0..2. .0..1..1..0
%Y Column 1 is A000302.
%Y Column 2 is A159739(n+1).
%Y Row 1 is A120926(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 21 2016
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