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%I #4 Mar 05 2016 19:28:34
%S 0,5,5,40,216,40,240,3096,3096,240,1280,39784,103296,39784,1280,6400,
%T 462680,3200604,3200604,462680,6400,30720,5145736,90748696,240637408,
%U 90748696,5145736,30720,143360,55265336,2472983556,16644595392
%N T(n,k)=Number of nXk 0..4 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling four exactly once.
%C Table starts
%C ......0..........5.............40................240...................1280
%C ......5........216...........3096..............39784.................462680
%C .....40.......3096.........103296............3200604...............90748696
%C ....240......39784........3200604..........240637408............16644595392
%C ...1280.....462680.......90748696........16644595392..........2840332868960
%C ...6400....5145736.....2472983556......1109236460528........467693538063508
%C ..30720...55265336....65284613232.....71730749075588......74936429415811576
%C .143360..580002280..1686961414812...4544255355000752...11771832152564634464
%C .655360.5978552216.42866673833128.283289815771686692.1821445245786662249776
%H R. H. Hardin, <a href="/A269829/b269829.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 8*a(n-1) -16*a(n-2)
%F k=2: [order 6] for n>7
%F k=3: [order 18] for n>19
%F k=4: [order 48] for n>49
%e Some solutions for n=3 k=4
%e ..0..0..3..3. .0..0..2..3. .0..0..2..3. .0..0..0..2. .0..1..4..1
%e ..1..0..2..3. .0..1..3..3. .0..0..2..3. .1..0..1..0. .0..0..1..1
%e ..1..1..3..3. .1..2..4..2. .3..3..3..0. .4..2..1..2. .0..1..2..1
%K nonn,tabl
%O 1,2
%A _R. H. Hardin_, Mar 05 2016