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A230977
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T(n,k)=Number of (n+2)X(k+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero
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9
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0, 16, 16, 64, 144, 64, 256, 1024, 1024, 256, 1344, 9216, 13872, 9216, 1344, 7056, 85264, 215296, 215296, 85264, 7056, 34944, 767376, 3512016, 6170256, 3512016, 767376, 34944, 173056, 6885376, 56791296, 190219264, 190219264, 56791296
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OFFSET
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1,2
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COMMENTS
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Table starts
......0.......16..........64...........256.............1344...............7056
.....16......144........1024..........9216............85264.............767376
.....64.....1024.......13872........215296..........3512016...........56791296
....256.....9216......215296.......6170256........190219264.........5771137024
...1344....85264.....3512016.....190219264......11094079744.......630277210000
...7056...767376....56791296....5771137024.....630277210000.....66985909298064
..34944..6885376...916182800..173342326336...35475345905904...7053147648320400
.173056.61968384.14798235904.5217149355664.2001432811365376.744552485586204304
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 4*a(n-1) +20*a(n-3) +25*a(n-4)
k=2: a(n) = 9*a(n-1) -8*a(n-2) +72*a(n-3) +9*a(n-4) -81*a(n-5)
k=3: [order 25]
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EXAMPLE
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Some solutions for n=1 k=4
..0..3..0..3..2..1....0..1..2..1..2..3....0..2..2..0..0..0....0..0..0..0..0..2
..2..1..0..3..2..1....0..1..2..3..0..1....1..1..3..3..1..1....3..1..1..3..3..1
..0..1..2..3..0..1....0..1..0..3..2..3....0..2..0..2..2..0....0..2..2..2..2..2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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