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A223680
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T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal
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11
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2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 316, 256, 32, 22, 256, 1118, 2032, 1024, 64, 29, 484, 3177, 9822, 13045, 4096, 128, 37, 841, 7745, 35509, 85663, 83737, 16384, 256, 46, 1369, 16857, 105995, 384009, 744272, 537496, 65536, 512, 56, 2116, 33615, 275775
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OFFSET
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1,1
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COMMENTS
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Table starts
....2.......4.........7.........11..........16...........22............29
....4......16........49........121.........256..........484...........841
....8......64.......316.......1118........3177.........7745.........16857
...16.....256......2032.......9822.......35509.......105995........275775
...32....1024.....13045......85663......384009......1363639.......4123210
...64....4096.....83737.....744272.....4106403.....17068664......58944337
..128...16384....537496....6458585....43632367....210660192.....821284360
..256...65536...3450100...56030742...462307835...2577807779...11265254628
..512..262144..22145617..486038270..4893189359..31402790284..152970187735
.1024.1048576.142149013.4215998078.51766786082.381690187059.2064772010660
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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)
k=2: a(n) = 4*a(n-1)
k=3: a(n) = 7*a(n-1) -3*a(n-2) -5*a(n-3) +2*a(n-4)
k=4: [order 9]
k=5: [order 19]
k=6: [order 36]
k=7: [order 70]
Empirical for row n:
n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1
n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1
n=3: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1
n=4: polynomial of degree 8
n=5: polynomial of degree 10 for n>2
n=6: polynomial of degree 12 for n>3
n=7: polynomial of degree 14 for n>4
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EXAMPLE
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Some solutions for n=3 k=4
..0..0..0..0....0..0..1..1....1..1..0..0....0..0..0..1....0..0..0..0
..1..0..0..0....0..1..1..0....0..1..1..0....1..1..0..0....1..0..0..0
..0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..0....1..1..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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