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A250797
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction
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15
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10, 24, 24, 54, 66, 58, 118, 162, 180, 140, 252, 376, 482, 490, 338, 530, 838, 1190, 1430, 1336, 816, 1102, 1818, 2776, 3776, 4258, 3646, 1970, 2272, 3868, 6230, 9258, 12062, 12706, 9956, 4756, 4654, 8114, 13598, 21610, 31220, 38676, 37986, 27194, 11482
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OFFSET
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1,1
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COMMENTS
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Table starts
....10.....24......54.....118......252......530......1102......2272......4654
....24.....66.....162.....376......838.....1818......3868......8114.....16842
....58....180.....482....1190.....2776.....6230.....13598.....29084.....61274
...140....490....1430....3776.....9258....21610.....48600....106426....228342
...338...1336....4258...12062....31220....76110....177142....398704....874298
...816...3646...12706...38676...105954...270598....653880...1517666...3411886
..1970...9956...37986..124366...361344...968942...2437366...5849556..13519146
..4756..27194..113694..400616..1236058..3485538...9144752..22741458..54152230
.11482..74288..340562.1292134..4237556.12580830..34478398..88996688.218754226
.27720.202950.1020650.4171276.14549610.45517150.130446176.349951066.889238238
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-2)
k=2: a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +2*a(n-4)
k=3: a(n) = 6*a(n-1) -10*a(n-2) +11*a(n-4) -6*a(n-5)
k=4: a(n) = 8*a(n-1) -20*a(n-2) +8*a(n-3) +33*a(n-4) -36*a(n-5) +8*a(n-7)
k=5: [order 9]
k=6: [order 11]
k=7: [order 13]
Empirical for row n:
n=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3)
n=2: a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4)
n=3: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5)
n=4: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-3) +9*a(n-4) +6*a(n-5) -8*a(n-6) -a(n-7) +2*a(n-8)
n=5: [order 9]
n=6: [order 12]
n=7: [order 13]
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..0..1..0....0..0..0..0..0....1..1..1..0..1....0..0..0..0..1
..0..0..0..0..1....0..0..0..0..0....1..1..1..0..0....0..0..0..0..0
..0..0..0..0..1....0..0..0..0..1....1..1..1..0..1....0..0..0..0..0
..1..1..1..1..0....0..0..0..0..1....1..1..1..0..1....0..0..1..1..1
..1..1..1..1..0....0..0..0..0..0....1..1..1..0..1....0..0..1..1..1
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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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