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%I #6 Feb 20 2016 06:48:07
%S 4,16,16,60,148,60,216,1164,1164,216,756,8532,18556,8532,756,2592,
%T 59916,275796,275796,59916,2592,8748,408596,3924212,8317996,3924212,
%U 408596,8748,29160,2727564,54199284,240647068,240647068,54199284,2727564,29160
%N T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.
%C Table starts
%C ......4........16............60..............216.................756
%C .....16.......148..........1164.............8532...............59916
%C .....60......1164.........18556...........275796.............3924212
%C ....216......8532........275796..........8317996...........240647068
%C ....756.....59916.......3924212........240647068.........14197016484
%C ...2592....408596......54199284.......6766301156........815458664276
%C ...8748...2727564.....732561916.....186315931804......45920055321732
%C ..29160..17914580....9740150372....5049212790572....2546667557472940
%C ..96228.116170764..127846717716..135126561336764..139535357045338964
%C .314928.745617300.1660741102212.3579710280903028.7570570235882777884
%H R. H. Hardin, <a href="/A269143/b269143.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -9*a(n-2)
%F k=2: a(n) = 12*a(n-1) -38*a(n-2) +12*a(n-3) -a(n-4) for n>5
%F k=3: [order 8] for n>9
%F k=4: [order 20] for n>22
%F k=5: [order 42] for n>45
%e Some solutions for n=3 k=4
%e ..0..3..2..3. .2..0..2..2. .0..0..0..2. .0..3..2..3. .0..2..2..2
%e ..2..3..2..2. .2..0..0..0. .0..0..0..2. .2..3..3..3. .0..0..0..2
%e ..2..2..3..3. .3..1..0..2. .1..1..0..1. .2..2..2..2. .0..2..2..2
%Y Column 1 is A120926(n+1).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 20 2016
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