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A270606
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T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1 or k-1 exactly once.
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12
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0, 0, 6, 0, 0, 0, 0, 36, 0, 0, 0, 36, 312, 0, 0, 0, 96, 1716, 8808, 0, 0, 0, 120, 8148, 171576, 443088, 0, 0, 0, 204, 23448, 1728288, 46957788, 44168712, 0, 0, 0, 252, 67788, 13177740, 1008327378, 38923001616, 8708857332, 0, 0, 0, 360, 144252, 70129212
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OFFSET
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1,3
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COMMENTS
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Table starts
.0.0........0...........0.............0...............0................0
.6.0.......36..........36............96.............120..............204
.0.0......312........1716..........8148...........23448............67788
.0.0.....8808......171576.......1728288........13177740.........70129212
.0.0...443088....46957788....1008327378.....25162747992.....271906503420
.0.0.44168712.38923001616.1749723617976.176610474548304.4288332432901128
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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) for n>5
n=3: [order 10] for n>17
n=4: [order 18] for n>33
Empirical quasipolynomials for row n:
n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2 for n>1
n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2 for n>7
n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2 for n>15
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EXAMPLE
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Some solutions for n=4 k=4
.....0........0........4........0........0........0........2........3
....0.4......0.1......0.4......0.0......0.0......0.1......0.1......1.1
...0.4.4....3.1.3....1.3.3....4.4.2....0.0.0....0.0.3....0.0.0....1.3.1
..0.0.0.3..1.3.3.4..3.1.1.3..2.0.4.3..0.1.4.2..4.0.1.3..0.4.4.0..0.0.1.3
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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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