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A270850
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T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1, k or k-1 exactly once.
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12
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0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 24, 30, 0, 0, 0, 66, 270, 252, 0, 0, 0, 120, 1650, 6822, 2298, 0, 0, 0, 198, 7344, 108348, 307494, 28440, 0, 0, 0, 288, 24954, 1144464, 15754872, 27582438, 460494, 0, 0, 0, 402, 68838, 8559378, 469037376, 5805948474, 4875050400
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OFFSET
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1,8
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COMMENTS
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Table starts
.0.0......0..........0.............0................0..................0
.0.0......6.........24............66..............120................198
.0.0.....30........270..........1650.............7344..............24954
.0.0....252.......6822........108348..........1144464............8559378
.0.0...2298.....307494......15754872........469037376.........8746813158
.0.0..28440...27582438....5805948474.....571228600932.....29999932959600
.0.0.460494.4875050400.5281372355106.2104222937252028.358240737864481086
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LINKS
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FORMULA
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Empirical for row n:
n=1: a(n) = a(n-1)
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
.....3........0........4........3........2........3........0........0
....4.3......0.1......4.4......4.4......4.4......4.4......0.0......1.2
...4.2.4....1.0.1....2.4.3....3.3.3....3.4.4....2.4.4....0.0.0....1.0.0
..3.4.4.3..2.0.1.0..4.2.4.3..2.4.4.3..4.2.4.2..0.4.4.2..2.1.0.2..0.1.1.1
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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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