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A270256
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T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k exactly once.
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12
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0, 0, 0, 0, 12, 0, 0, 24, 66, 0, 0, 48, 768, 468, 0, 0, 72, 4428, 37848, 3612, 0, 0, 108, 14976, 772056, 3280968, 40020, 0, 0, 144, 42750, 7876728, 308256072, 534438768, 601368, 0, 0, 192, 96768, 51535116, 12712991544, 302595682944, 168922341960
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OFFSET
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1,5
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COMMENTS
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Table starts
.0.....0.........0............0..............0................0
.0....12........24...........48.............72..............108
.0....66.......768.........4428..........14976............42750
.0...468.....37848.......772056........7876728.........51535116
.0..3612...3280968....308256072....12712991544.....233617868244
.0.40020.534438768.302595682944.67475902622400.4283012188676772
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LINKS
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FORMULA
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Empirical for row n:
n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
n=3: [order 10]
n=4: [order 18]
Empirical quasipolynomials for row n:
n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2
n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2
n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2
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EXAMPLE
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Some solutions for n=3 k=4
....0......2......2......2......4......1......3......2......3......0......3
...1.1....1.3....0.0....4.1....4.3....4.0....3.2....2.1....4.3....4.2....1.0
..0.4.4..1.2.0..2.2.1..3.1.2..3.0.2..2.1.0..4.0.1..1.4.2..3.0.3..3.3.4..1.0.2
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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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