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A250898
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T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing 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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37, 127, 125, 403, 431, 413, 1229, 1325, 1450, 1333, 3673, 3867, 4388, 4750, 4213, 10875, 11029, 12387, 14196, 15111, 13111, 32095, 31215, 33821, 39003, 44525, 47061, 40357, 94729, 88421, 91030, 102789, 119359, 136509, 144442, 123271, 280069
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OFFSET
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1,1
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COMMENTS
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Table starts
......37.....127......403.....1229.....3673.....10875.....32095.....94729
.....125.....431.....1325.....3867....11029.....31215.....88421....251819
.....413....1450.....4388....12387....33821.....91030....244200....657443
....1333....4750....14196....39003...102789....265546....680504...1742387
....4213...15111....44525...119359...305429....764315...1893433...4673299
...13111...47061...136509...357335...890199...2168405...5232461..12579759
...40357..144442...412006..1052787..2553537...6060594..14283986..33622407
..123271..439056..1231112..3069907..7243359..16732140..38498188..88810083
..374509.1326285..3657629..8903447.20421217..45832201.102731213.231909787
.1133503.3990883.10837431.25780959.57483879.125162059.272597111.600517559
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..180
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FORMULA
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Empirical for column k (k=2 recurrence works also for k=1):
k=1: a(n) = 8*a(n-1) -23*a(n-2) +28*a(n-3) -12*a(n-4) for n>6
k=2-7: a(n) = 12*a(n-1) -60*a(n-2) +162*a(n-3) -255*a(n-4) +234*a(n-5) -116*a(n-6) +24*a(n-7) for n>9
Empirical for row n (n=3 recurrence works also for n=1,2):
n=1: a(n) = 9*a(n-1) -31*a(n-2) +51*a(n-3) -40*a(n-4) +12*a(n-5)
n=2: a(n) = 10*a(n-1) -40*a(n-2) +82*a(n-3) -91*a(n-4) +52*a(n-5) -12*a(n-6)
n=3-7: a(n) = 14*a(n-1) -85*a(n-2) +294*a(n-3) -639*a(n-4) +906*a(n-5) -839*a(n-6) +490*a(n-7) -164*a(n-8) +24*a(n-9)
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EXAMPLE
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Some solutions for n=4 k=4
..0..0..1..0..1....1..1..0..0..0....1..1..1..1..0....2..2..1..0..0
..0..0..1..0..1....1..1..1..1..1....2..2..2..2..2....1..1..2..1..1
..1..1..2..1..2....1..1..1..1..1....0..0..0..0..0....1..1..2..1..1
..1..1..2..1..2....2..2..2..2..2....0..1..1..1..1....0..0..1..0..0
..1..1..2..1..2....0..0..0..0..0....0..1..1..2..2....0..1..2..2..2
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CROSSREFS
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Sequence in context: A044669 A048510 A250891 * A165811 A142331 A250899
Adjacent sequences: A250895 A250896 A250897 * A250899 A250900 A250901
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KEYWORD
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nonn,tabl
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AUTHOR
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R. H. Hardin, Nov 28 2014
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STATUS
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approved
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