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A258554
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T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically
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15
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16, 44, 44, 104, 112, 104, 228, 210, 296, 228, 480, 344, 598, 652, 480, 988, 506, 985, 1244, 1329, 988, 2008, 683, 1403, 1891, 2384, 2530, 2008, 4052, 894, 1917, 2509, 3754, 3980, 4667, 4052, 8144, 1140, 2542, 3314, 5070, 6196, 6348, 8419, 8144, 16332, 1421
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OFFSET
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1,1
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COMMENTS
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Table starts
....16....44...104...228...480...988..2008..4052..8144..16332..32712..65476
....44...112...210...344...506...683...894..1140..1421...1725...2071...2460
...104...296...598...985..1403..1917..2542..3222..3940...4767...5718...6737
...228...652..1244..1891..2509..3314..4313..5356..6331...7470...8820..10231
...480..1329..2384..3754..5070..6662..8612.10720.12831..15045..17532..20200
...988..2530..3980..6196..8339.10854.13833.17058.20414..23858..27446..31237
..2008..4667..6348..9688.12940.16942.21653.26628.31806..37351..43158..49004
..4052..8419..9567.14216.18630.24300.31254.38451.45713..53599..62205..70891
..8144.14932.13847.20285.26240.33844.43655.54137.64507..75625..87878.100660
.16332.26184.19227.27687.35386.45166.57928.71823.85853.100830.116939.133789
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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) -5*a(n-2) +2*a(n-3)
k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +3*a(n-4) -4*a(n-5) +2*a(n-6) +2*a(n-7) -3*a(n-8) +a(n-9) for n>11
k=3: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>11
k=4: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>12
k=5: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>13
k=6: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>14
k=7: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -4*a(n-5) +6*a(n-6) -4*a(n-7) +a(n-8) for n>15
Empirical for row n:
n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)
n=2: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>10
n=3: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>10
n=4: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>11
n=5: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>12
n=6: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>13
n=7: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +a(n-4) -3*a(n-5) +3*a(n-6) -a(n-7) for n>14
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EXAMPLE
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Some solutions for n=4 k=4
..1..0..0..0..1....0..0..0..0..1....1..0..0..0..0....0..0..0..0..0
..1..0..0..0..1....0..0..0..0..0....1..0..0..0..0....1..0..0..0..0
..1..0..0..0..1....1..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..0..0..1..1....1..1..1..1..1....1..1..0..0..0....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..0....1..0..0..0..0....0..0..0..0..0
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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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