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A269829 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. 9

%I

%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

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)