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A250942
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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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14
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37, 155, 125, 599, 699, 413, 2247, 3355, 2812, 1333, 8189, 15431, 16208, 10528, 4213, 29281, 67595, 87529, 71014, 37477, 13111, 103093, 287045, 442409, 444421, 289407, 128507, 40357, 358683, 1188599, 2130148, 2572787, 2067987, 1115035, 428095
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OFFSET
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1,1
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COMMENTS
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Table starts
......37......155.......599.......2247........8189........29281........103093
.....125......699......3355......15431.......67595.......287045.......1188599
.....413.....2812.....16208......87529......442409......2130148.......9865706
....1333....10528.....71014.....444421.....2572787.....14019652......72722706
....4213....37477....289407....2067987....13550488.....82716842.....475951361
...13111...128507...1115035....8976385....65910564....447407616....2839711239
...40357...428095...4106983...36809498...300230097...2251710502...15686582837
..123271..1394237..14585505..144007880..1294549437..10665462156...81197881457
..374509..4460779..50276307..541598982..5327479262..47958734697..397409857238
.1133503.14073313.169096201.1969991292.21062394646.206139574253.1852256126330
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..144
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FORMULA
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Empirical for column k:
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: [order 7] for n>11
k=3: [order 15] for n>21
k=4: [order 21] for n>29
k=5: [order 27] for n>37
k=6: [order 33] for n>45
k=7: [order 39] for n>53
Empirical for row n:
n=1: a(n) = 6*a(n-1) -6*a(n-2) -15*a(n-3) +14*a(n-4) +12*a(n-5)
n=2: [order 11]
n=3: [order 21]
n=4: [order 38]
n=5: [order 60]
n=6: [order 88]
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EXAMPLE
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Some solutions for n=3 k=4
..2..1..0..0..2....0..0..1..1..1....1..2..0..0..2....2..0..0..1..0
..2..1..0..0..2....0..0..1..2..0....2..1..1..1..1....2..0..0..1..0
..2..1..0..1..1....0..0..1..2..0....2..1..2..2..0....2..0..0..2..2
..2..1..0..1..2....1..1..2..1..1....2..1..2..2..0....2..0..0..2..2
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CROSSREFS
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Column 1 is A250891
Sequence in context: A158596 A142688 A178835 * A250943 A142197 A140011
Adjacent sequences: A250939 A250940 A250941 * A250943 A250944 A250945
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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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