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A223789
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T(n,k)=Number of nXk 0..2 arrays with rows, diagonals and antidiagonals unimodal
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12
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3, 9, 9, 22, 81, 27, 46, 484, 729, 81, 86, 2116, 8635, 6561, 243, 148, 7396, 62365, 151580, 59049, 729, 239, 21904, 334230, 1560013, 2703137, 531441, 2187, 367, 57121, 1455816, 11012718, 39387861, 48302789, 4782969, 6561, 541, 134689, 5425943
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OFFSET
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1,1
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COMMENTS
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Table starts
.....3..........9............22..............46................86
.....9.........81...........484............2116..............7396
....27........729..........8635...........62365............334230
....81.......6561........151580.........1560013..........11012718
...243......59049.......2703137........39387861.........343454446
...729.....531441......48302789......1026135371.......11150023974
..2187....4782969.....862007289.....27088106846......377163884938
..6561...43046721...15379566078....715394830136....12972494260444
.19683..387420489..274427327200..18858304684055...446829906314726
.59049.3486784401.4896915028511.496722962933967.15355124632228358
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LINKS
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FORMULA
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Empirical for column k:
k=1: a(n) = 3*a(n-1)
k=2: a(n) = 9*a(n-1)
k=3: [order 15]
k=4: [order 80]
Empirical: rows n=1..5 are polynomials of order 4*n for k>0,0,1,8,15
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EXAMPLE
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Some solutions for n=3 k=4
..2..2..2..1....1..2..0..0....1..1..2..2....1..2..1..1....0..0..0..0
..0..2..2..1....0..0..1..0....0..2..2..1....1..1..2..0....0..1..2..0
..2..1..0..0....0..1..0..0....0..2..0..0....2..2..2..2....0..0..1..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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